{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(section:fixed-point-iteration)=\n",
    "# Solving Equations by Fixed Point Iteration (of Contraction Mappings)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Last revised on August 27, 2025**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References:** \n",
    "\n",
    "- {cite}`Sauer` Section 1.2, *Fixed Point Iteration*.\n",
    "\n",
    "- {cite}`Burden-Faires` Section 2.2, *Fixed Point Iteration*.\n",
    "\n",
    "- {cite}`Dionne` Sections 2.4, *Fixed Point Method*, and 2.7, *Order of Convergence*.\n",
    "\n",
    "- {cite}`Dahlquist-Bjorck-v1` Sections 1.1.2 and 6.1.4."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "In the next section we will meet [Newton's method for root-finding](section:newtons-method),\n",
    "which you might have seen in a calculus course.\n",
    "This is one very important example of a more general strategy of **fixed-point iteration**, so we start with that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyPlot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fixed-point form for equations\n",
    "\n",
    "A variant of stating equations as *root-finding* ($f(x) = 0$) is *fixed-point* form:\n",
    "given a function $g:\\mathbb{R} \\to \\mathbb{R}$ or $g:\\mathbb{C} \\to \\mathbb{C}$\n",
    "(or even $g:\\mathbb{R}^n \\to \\mathbb{R}^n$; a later topic),\n",
    "find a *fixed point* of $g$.\n",
    "That is, a value $p$ for its argument such that\n",
    "\n",
    "$$g(p) = p$$\n",
    "\n",
    "Such problems are interchangeable with root-finding.\n",
    "One way to convert from $f(x) = 0$ to $g(x) = x$ is functionining\n",
    "\n",
    "$$g(x) := x - w(x) f(x)$$\n",
    "\n",
    "for any \"weight function\" $w(x)$.\n",
    "\n",
    "One can convert the other way too, for example functionining $f(x) := g(x) - x$.\n",
    "We have already seen this when we converted the equation $x = \\cos x$ to $f(x) = x - \\cos x = 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the two setups graphically: in each case, the $x$ value at the intersection of the two curves is the solution we seek."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "f(x) = x - cos.(x)\n",
    "g(x) = cos.(x);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = -1.0\n",
    "b = 1.0\n",
    "x = range(a, b, 100);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x600 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 600x600 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(10,6))\n",
    "title(\"Zeros of \" * L\"y = f(x) = x - \\cos(x)\")\n",
    "plot(x, f.(x))\n",
    "plot([a, b], [0, 0])\n",
    "grid(true)\n",
    "\n",
    "figure(figsize=(6,6))\n",
    "title(\"Fixed points of \" * L\"y = g(x) = \\cos(x)\")\n",
    "plot(x, g.(x))\n",
    "plot(x, x)\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fixed-point iteration\n",
    "\n",
    "Fixed point form can be convenient partly because we almost always have to solve by successive approximations,\n",
    "or *iteration*, and fixed point form suggests _one_ choice of iterative procedure:\n",
    "start with any first approximation $x_0$, and iterate with\n",
    "\n",
    "$$\n",
    "x_1 = g(x_0), \\, x_2 = g(x_1), \\dots, x_{k+1} = g(x_k), \\dots\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proposition}\n",
    ":label: proposition-1-fpi-iterates-converge-to-fp\n",
    "\n",
    "If $g$ is continuous, and **if** the above sequence $\\{x_0, x_1, \\dots \\}$ converges to a limit $p$, then that limit is a fixed point of function $g$: $g(p) = p$.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proof}\n",
    "From $\\displaystyle \\lim_{k \\to \\infty} x_k = p$, continuity gives\n",
    "\n",
    "$$\\lim_{k \\to \\infty} g(x_k) = g(p).$$\n",
    "\n",
    "On the other hand, $g(x_k) = x_{k+1}$, so\n",
    "\n",
    "$$\\lim_{k \\to \\infty} g(x_k) = \\lim_{k \\to \\infty} x_{k+1} = p.$$\n",
    "\n",
    "Comparing gives $g(p) = p$.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mappings and contraction mappings\n",
    "\n",
    "That second \"if\" is a big one.\n",
    "Fortunately, it can often be resolved using the idea of a *contraction mapping*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:definition} Mapping\n",
    ":label: definition-mapping\n",
    "\n",
    "A function $g(x)$ defined on a closed interval $D = [a, b]$ which sends values back into that interval,\n",
    "$g: D \\to D$, is sometimes called a *map* or *mapping*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:remark}\n",
    ":label: remark-1-fixed-point-iteration\n",
    "\n",
    "The same applies for a function $g: D \\to D$ where $D$ is a subset of the complex numbers,\n",
    "or even of the vectors $\\mathbb{R}^n$ or $\\mathbb{C}^n$. This will help later with solving more general types of equations.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A mapping is sometimes thought of as moving a region $S$ within its domain $D$ to another such region, by moving each point\n",
    "$x \\in S \\subset D$\n",
    "to its image\n",
    "$g(x) \\in g(S) \\subset D$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proposition}\n",
    ":label: proposition-2-ivp-fpi-version\n",
    "\n",
    "Any continuous mapping on a closed interval $[a, b]$ has at least one fixed point.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proof}\n",
    "Consider the \"root-finding cousin\", $f(x) = x - g(x)$.\n",
    "\n",
    "First, $f(a) = a - g(a) \\leq 0$, since $g(a) \\geq a$ so as to be in the domain $[a,b]$ — similarly, $f(b) = b - g(b) \\geq 0$.\n",
    "\n",
    "From the Intermediate Value Theorem, $f$ has a zero $p$, where $f(p) = p - g(p) = 0$.\n",
    "\n",
    "In other words, the graph of $y=g(x)$ goes from being above the line $y=x$ at $x=a$ to below it at $x=b$,\n",
    "so at some point $x=p$, the curves meet: $y = x = p$ and $y = g(p)$, so $p = g(p)$.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example}\n",
    ":label: example-1-x-4cosx\n",
    "\n",
    "Let us illustrate this with the mapping $g4(x) := 4 \\cos x$,\n",
    "for which the fact that $|g4(x)| \\leq 4$ ensures that this is a map of the domain $D = [-4, 4]$ into itself:\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "g_4(x) = 4cos(x)\n",
    "a = -4.0\n",
    "b = 4.0;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 700x700 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = range(a, b, 100);\n",
    "figure(figsize=[7,7])\n",
    "title(L\"Fixed points of the map $g_4(x) = 4 \\cos(x)$\")\n",
    "plot(x, g_4.(x), label=L\"y = g_4(x)\")\n",
    "plot(x, x, label=\"y=x\")\n",
    "legend()\n",
    "grid(true);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example has multiple fixed points (three of them).\n",
    "To ensure both the existence of a **unique** solution, and covergence of the iteration to that solution, we need an extra condition."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:definition} Contraction Mapping\n",
    ":label: definition-contraction-mapping\n",
    "\n",
    "A mapping $g:D \\to D$, is called a **contraction** or **contraction mapping** if there is a constant $C < 1$ such that\n",
    "\n",
    "$$|g(x) - g(y)| \\leq C |x - y|$$\n",
    "\n",
    "for any $x$ and $y$ in $D$.\n",
    "We then call $C$ a *contraction constant*.\n",
    "\n",
    "(*Aside:* The same applies for a domain in $\\mathbb{R}^n$: just replace the absolute value $| \\dots |$ by the vector norm\n",
    "$\\| \\dots \\|$.)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:remark}\n",
    ":label: remark-2-fixed-point-iteration\n",
    "\n",
    "- It is not enough to have $| g(x) - g(y) | < | x - y |$ or $C = 1$!\n",
    "We need the ratio\n",
    "$\\displaystyle \\frac{|g(x) - g(y)|}{|x - y|}$\n",
    "to be *uniformly* less than one for all possible values of $x$ and $y$.\n",
    "\n",
    "- The same concept applies for a domain in $\\mathbb{C}$, $\\mathbb{R}^n$ or $\\mathbb{C}^n$:\n",
    "for vectors, just replace the absolute value $| \\dots |$ by the vector norm $\\| \\dots \\|$.\n",
    "In fact, we will sometimes blur the distinction by using the \"single line\" absolute value notation for vector norms too.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:theorem} A Contraction Mapping Theorem\n",
    ":label: a-contraction-mapping-theorem\n",
    "\n",
    "Any contraction mapping on a closed, bounded interval $D = [a, b]$ has exactly one fixed point $p$ in $D$.\n",
    "Further, this can be calculated as the limit $\\displaystyle p = \\lim_{k \\to \\infty} x_k$ of the iteration sequence given by $x_{k+1} = g(x_{k})$ for *any* choice of the starting point $x_{0} \\in D$.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proof}\n",
    "\n",
    "First, uniqeness:\n",
    "(the main idea of the proof can be shown with the help of a few pictures.)\n",
    "\n",
    "between any two of the multiple fixed points above — call them $p_0$ and $p_1$ — the graph of $g(x)$ has to rise with secant slope 1: $(g(p_1) - g(p_0)/(p_1 - p_0) = (p_1 - p_0)/(p_1 - p_0) = 1$, and this violates the contraction property.\n",
    "\n",
    "So instead, for a contraction, the graph of a contraction map looks like the one below for our favorite example,\n",
    "$g(x) = \\cos x$ (which we will soon verify to be a contraction on interval $[-1, 1]$).\n",
    "\n",
    "The second claim, about **convergence** to the fixed point from any initial approximation $x_0$,\n",
    "will be verified below, once we have seen some ideas about measuring errors.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## An easy way of checking whether a differentiable function is a contraction\n",
    "\n",
    "With differentiable functions, the contraction condition can often be easily verified using derivatives:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:theorem} A derivative-based fixed point theorem\n",
    ":label: a-derivative-based-fixed-point-theorem\n",
    "\n",
    "If a function $g:[a,b] \\to [a,b]$ is differentiable and there is a constant $C < 1$ such that $|g'(x)| \\leq C$ for all $x \\in [a, b]$, then $g$ is a contraction mapping, and so has a unique fixed point in this interval.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proof}\n",
    "\n",
    "Using the Mean Value Theorem, $g(x) - g(y) = g'(c)(x - y)$ for some $c$ between $x$ and $y$.\n",
    "Then taking absolute values,\n",
    "\n",
    "$$|g(x) - g(y)| = |g'(c)| \\cdot |(x - y)| \\leq C |(x - y)|.$$\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:remark}\n",
    "\n",
    "There is a partial converse:\n",
    "if $|g'(p)| > 1$ at a fixed point $p$, the contraction mapping will not converge to that fixed point, and in fact will diverge from it,\n",
    "as illustrated in {prf:ref}`example-4` below.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example} $g(x) = \\cos(x)$ is a contraction on interval $[-1,1]$\n",
    ":label: example-2-x-cosx\n",
    "\n",
    "Our favorite example $g(x) = \\cos(x)$ is a contraction, but we have to be a bit careful about the domain.\n",
    "\n",
    "For all real $x$, $g'(x) = -\\sin x$, so $|g'(x)| \\leq 1$; this is almost but not quite enough.\n",
    "\n",
    "However, we have seen that iteration values will settle in the interval $D = [-1,1]$,\n",
    "and considering $g$ as a mapping of this domain,\n",
    "$|g'(x)| \\leq \\sin(1) = 0.841\\dots < 1$: that is, now we have a contraction, with $C = \\sin(1) \\approx 0.841$.\n",
    "\n",
    "And as seen in the graph above, there is indeed a unique fixed point.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The contraction constant $C$ as a measure of how fast the approximations improve (the smaller the better)\n",
    "\n",
    "It can be shown that if $C$ is small (at least when one looks only at a reduced domain $|x - p| < R$) then the convergence is \"fast\" once $|x_k - p| < R$.\n",
    "\n",
    "To see this, we define some jargon for talking about errors.\n",
    "(For more details on error concepts, see section {doc}`error-measures-convergence-rates`.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:definition} Error\n",
    ":label: definition-error\n",
    "\n",
    "The *error* in $\\tilde x$ as an approximation to an exact value $x$ is\n",
    "\n",
    "$$\\text{error} := \\text{(approximation)} - \\text{(exact value)} = \\tilde x - x$$\n",
    "\n",
    "This will often be abbreviated as $E$.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:definition} Absolute Error\n",
    ":label: definition-absolute-error\n",
    "\n",
    "The *absolute error* in $\\tilde x$ an approximation to an exact value $x$ is the magnitude of the error:\n",
    "the absolute value $|E| = |\\tilde x - x|$.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:remark}\n",
    ":label: remark-3-fixed-point-iteration\n",
    "\n",
    "This will later be extended to $x$ and $\\tilde x$ being vectors,\n",
    "by again using the vector norm in place of the absolute value.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the case of $x_k$ as an approximation of $p$, we name the error $E_k := x_k - p$.\n",
    "Then $C$ measures a worst case for how fast the error decreases as $k$ increases, and this is \"exponentially fast\":"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proposition}\n",
    ":label: proposition-3\n",
    "\n",
    "$|E_{k+1}| \\leq C |E_{k}|$, or $|E_{k+1}|/|E_{k}|\\leq C$,\n",
    "and so\n",
    "\n",
    "$$|E_k| \\leq C^k |x_0 - p|$$\n",
    "\n",
    "That is, the error decreases at worst in a geometric sequence,\n",
    "which is exponential decrease with respect to the variable $k$.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proof}\n",
    "\n",
    "$E_{k+1} = x_{k+1} - p = g(x_{k}) - g(p)$, using $g(p) = p$.\n",
    "Thus the contraction property gives\n",
    "\n",
    "$$|E_{k+1}| = |g(x_k) - g(p)| \\leq C |x_k - p| = C |E_k|$$\n",
    "\n",
    "Applying this again,\n",
    "\n",
    "$$|E_k| \\leq C |E_{k-1}| \\leq C \\cdot C |E_{k-2}| = C^2 |E_{k-2}|$$\n",
    "\n",
    "and repeating $k-2$ more times,\n",
    "\n",
    "$$|E_k|\\leq  C^k |E_0| = C^k |x_0 - p|.$$\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:remark}\n",
    "We will often use this \"recursive\" strategy of relating the error in one iterate to that in the previous iterate.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now complete the proof of the above contraction mapping theorem {prf:ref}`a-contraction-mapping-theorem`:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proof}\n",
    "\n",
    "This now follows from {prf:ref}`proposition-3`:\n",
    "\n",
    "For **any** initial approximation $x_0$, we know that $|E_k|\\leq C^k |x_0 - p|$,\n",
    "and with $C < 1$, this can be made as small as we want by choosing a large enough value of $k$.\n",
    "Thus\n",
    "\n",
    "$$\\lim_{k \\to \\infty} |E_k| = \\lim_{k \\to \\infty} |x_k - p| = 0,$$\n",
    "which is another way of saying that $\\displaystyle \\lim_{k \\to \\infty} x_k = p$, or $x_k \\to p$, as claimed.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example} Solving $x = \\cos x$ with a naive fixed point iteration\n",
    ":label: example-3-x-cosx-fpi\n",
    "\n",
    "We have seen that _one_ way to convert the example\n",
    "$f(x) = x - \\cos x = 0$ to a fixed point iteration is $g(x) = \\cos x$,\n",
    "and that this is a contraction on $D = [-1, 1]$\n",
    "\n",
    "Here is what this iteration looks like:\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "UndefVarError: `g_1` not defined in `Main`\nSuggestion: check for spelling errors or missing imports.",
     "output_type": "error",
     "traceback": [
      "UndefVarError: `g_1` not defined in `Main`\nSuggestion: check for spelling errors or missing imports.",
      "",
      "Stacktrace:",
      " [1] top-level scope",
      "   @ In[23]:11"
     ]
    }
   ],
   "source": [
    "a = 0.0\n",
    "b = 1.0\n",
    "x = range(a, b, 100)\n",
    "iterations = 10\n",
    "\n",
    "# Start at left\n",
    "x_k = a\n",
    "figure(figsize=[7,7])\n",
    "title(L\"Solving $x = \\cos(x)$ starting to the left, at $x_0 =$\"*\" $a\")\n",
    "plot(x, x, \"g\")\n",
    "plot(x, g_1.(x), \"r\")\n",
    "grid(true)\n",
    "println(\"x_0 = $x_k\")\n",
    "for k in 1:iterations\n",
    "    g_x_k = g_1(x_k)\n",
    "    # Graph evalation of g(x_k) from x_k:\n",
    "    plot([x_k, x_k], [x_k, g_1(x_k)], \"b\")\n",
    "    x_k_plus_1 = g_1(x_k)\n",
    "    #Connect to the new x_k on the line y = x:\n",
    "    plot([x_k, g_1(x_k)], [x_k_plus_1, x_k_plus_1], \"b\")\n",
    "    # Update names: the old x_k+1 is the new x_k\n",
    "    x_k = x_k_plus_1\n",
    "    println(\"x_$(k) = $x_k\")\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "UndefVarError: `g_1` not defined in `Main`\nSuggestion: check for spelling errors or missing imports.",
     "output_type": "error",
     "traceback": [
      "UndefVarError: `g_1` not defined in `Main`\nSuggestion: check for spelling errors or missing imports.",
      "",
      "Stacktrace:",
      " [1] top-level scope",
      "   @ In[24]:7"
     ]
    }
   ],
   "source": [
    "# Start at right\n",
    "x_k = b\n",
    "figure(figsize=[7,7])\n",
    "title(\"Solving \" * L\"x = \\cos(x)\" * \" starting to the right, at \" * L\"x_0 = \" * \"$b\")\n",
    "# Julia note: \"*\" is concatenation of strings\n",
    "plot(x, x, \"g\")\n",
    "plot(x, g_1.(x), \"r\")\n",
    "grid(true)\n",
    "println(\"x_0 = $x_k\")\n",
    "for k in 1:iterations\n",
    "    g_x_k = g_1(x_k)\n",
    "    # Graph evalation of g(x_k) from x_k:\n",
    "    plot([x_k, x_k], [x_k, g_1(x_k)], \"b\")\n",
    "    x_k_plus_1 = g_1(x_k)\n",
    "    #Connect to the new x_k on the line y = x:\n",
    "    plot([x_k, g_1(x_k)], [x_k_plus_1, x_k_plus_1], \"b\")\n",
    "    # Update names: the old x_k+1 is the new x_k\n",
    "    x_k = x_k_plus_1\n",
    "    println(\"x_$(k) = $x_k\")\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In each case, one gets a \"box spiral\" in to the fixed point.\n",
    "It always looks like this when $g$ is *decreasing* near the fixed point.\n",
    "\n",
    "If instead $g$ is *increasing* near the fixed point, the iterates approach monotonically, either from above or below:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example} Solving $f(x) = x^2 - 5x + 4 = 0$ in interval $[0, 3]$\n",
    ":label: example-4\n",
    "\n",
    "The roots are 1 and 4; for now we aim at the first of these,\n",
    "so we chose a domain $[0, 3]$ that contains just this root.\n",
    "\n",
    "Let us get a fixed point for by \"partially solving for $x$\": solving for the $x$ in the $5 x$ term:\n",
    "\n",
    "$$x = g(x) = (x^2 + 4)/5$$\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "f_2(x) = x^2 - 5*x + 4;\n",
    "g_2(x) = (x^2 + 4)/5;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 0.0;\n",
    "b = 3.0;\n",
    "x = range(a, b, 100);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x600 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[10,6])\n",
    "title(L\"Solving $y = f_2(x) = x^2-5x+4 = 0$\")\n",
    "plot(x, f_2.(x))\n",
    "plot([a, b], [0, 0])\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x600 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[10,6])\n",
    "title(L\"Finding fixed point of $y = g_2(x) = (x^2 + 4)/5$\")\n",
    "plot(x, g_2.(x))\n",
    "plot(x, x)\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "iterations = 10\n",
    "a = 0.0\n",
    "b = 1.5\n",
    "x = range(a, b, 100);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_0 = 0.0\n",
      "x_1 = 0.8\n",
      "x_2 = 0.9280000000000002\n",
      "x_3 = 0.9722368000000001\n",
      "x_4 = 0.9890488790548482\n",
      "x_5 = 0.9956435370319303\n",
      "x_6 = 0.9982612105666906\n",
      "x_7 = 0.9993050889044148\n",
      "x_8 = 0.999722132142052\n",
      "x_9 = 0.9998888682989302\n",
      "x_10 = 0.999955549789623\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 700x700 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Start at left\n",
    "x_k = a\n",
    "figure(figsize=[7,7])\n",
    "title(L\"Starting to the left, at $x_0 =$\"*\"$a\")\n",
    "grid(true)\n",
    "plot(x, x, \"g\")\n",
    "plot(x, g_2.(x), \"r\")\n",
    "println(\"x_0 = $x_k\")\n",
    "for k in 1:iterations\n",
    "    g_x_k = g_2(x_k)\n",
    "    # Graph evalation of g(x_k) from x_k:\n",
    "    plot([x_k, x_k], [x_k, g_2(x_k)], \"b\")\n",
    "    x_k_plus_1 = g_2(x_k)\n",
    "    #Connect to the new x_k on the line y = x:\n",
    "    plot([x_k, g_2(x_k)], [x_k_plus_1, x_k_plus_1], \"b\")\n",
    "    # Update names: the old x_k+1 is the new x_k\n",
    "    x_k = x_k_plus_1\n",
    "    println(\"x_$(k) = $x_k\")\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_0 = 3.0\n",
      "x_1 = 2.6\n",
      "x_2 = 2.152\n",
      "x_3 = 1.7262208\n",
      "x_4 = 1.3959676500705283\n",
      "x_5 = 1.1897451360086866\n",
      "x_6 = 1.0830986977312658\n",
      "x_7 = 1.0346205578054328\n",
      "x_8 = 1.014087939726725\n",
      "x_9 = 1.0056748698998388\n",
      "x_10 = 1.0022763887896116\n"
     ]
    },
    {
     "data": {
      "image/png": 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LmzevU4OUr68vefPm1Ql+F9SOjqF2dAy1o2OoHR1D7eg4mdWWaRlOpMHmIiIiIhmkICUiIiKSQQpSIiIiIhmkICUiIiKSQQpSIiIiIhmkICUiIiKSQQpSIiIiIhmkICUiIiKSQQpSIiIiIhmkICUiIiKSQQpSIiIiIhmkICUiIiKSQQpSIiIiIhmkICUiIiKSQQpSIiIiIhmkICUiIiKSQQpSIiIiIhmUriA1depUatasSd68ecmbNy/169dnw4YNt/3Mtm3bqFu3Lj4+PlSoUIFp06bdVcEiIiIiriJdQap06dK888477N69m927d9O4cWPatWvHr7/+mur2R48epWXLljRs2JC9e/cyevRohgwZwrJlyxxSvIiIiIiVPNKzcZs2bVIsv/XWW0ydOpVvv/2W6tWr37T9tGnTKFu2LJMmTQKgatWq7N69m4kTJ9KxY8eMVy0iIiICGIYBgM1ms+T4GR4jlZiYyKJFi4iOjqZ+/fqpbrNr1y4CAwNTrAsKCmL37t3Y7faMHlpERERyqKQkg8lff8mFazH8L0NZFqIgnT1SAPv376d+/frExsbi5+fHihUrqFatWqrbnj17lmLFiqVYV6xYMRISEoiMjKREiRKpfi4uLo64uLjk5aioKADsdrvTAtiN/Srg3R21o2OoHR1D7egYakfHUDvePcMwGLXxTT5s9zoAzRtfolhhP4cfJz1/RukOUpUrV2bfvn1cvnyZZcuWERwczLZt224Zpv6bEtPSBTdhwgTGjx9/0/rQ0FB8fX3TW3K6hIWFOXX/OYXa0THUjo6hdnQMtaNjqB0zxjAM5p+dz9KT6wEzSH2z/Rt8fBIdfqyYmJg0b2szbiSbDGratCn33nsvn3/++U2/e/zxx6lduzaTJ09OXrdixQq6dOlCTEwMnp6eqe4ztR6pMmXKEBkZSd68ee+m3Fuy2+2EhYXRrFmzW9Yld6Z2dAy1o2OoHR1D7egYaseMMwyDMRFjeH/X+xDvC29HA3D+fAz58zu+LaOioihcuDBXrly5Y+5Id4/UfxmGkSL0/Fv9+vVZs2ZNinWhoaHUq1fvtieRt7c33t7eN6339PR0+smXGcfICdSOjqF2dAy1o2OoHR1D7Zg+hmHwyuZXzBAFvN9sIi+9bf7OWW2Znn2ma7D56NGj2bFjB8eOHWP//v28+uqrRERE0LNnTwBGjRpFnz59krcfMGAAx48fZ/jw4Rw4cICZM2cyY8YMRowYkZ7DioiISA5kGAYvb36Z93a+B8AnLT7huQefs7iqlNLVI3Xu3Dl69+7NmTNnyJcvHzVr1mTjxo00a9YMgDNnznDixInk7cuXL8/69esZNmwYn332GSVLluTjjz/W1AciIiJyW4Zh8FLYS3yw6wMAPm3xKYMeGkR0tMWF/Ue6gtSMGTNu+/vZs2fftK5Ro0b8+OOP6SpKREREci7DMHgx9EU++vYjAKa0nOJyPVE33PUYKRERERFHMQyD4ZuGM+m7SQBMazWNZ+s9a21Rt6EgJSIiIi7BMAyGbhzKx99/DMDnrT/nmbrPWFzV7SlIiYiIiOUMw+CFjS/wyfefADC9zXT61+lvcVV3piAlIiIiljIMg+c3PM9nP3yGDRvT20ynX51+VpeVJgpSIiIiYhnDMBi8fjBTdk/Bho0v235J39p9rS4rzRSkRERExBJJRhKD1w9m6u6p2LAxs91Mnqz1pNVlpYuClIiIiGS6JCOJQesGMW3PNGzYmNVuFsG1gq0uK90UpERERCRTJRlJDFw3kM/3fI4NGyHtQ+j9QG+ry8oQBSkRERHJNElGEgPWDmD6j9Nxs7kR0j6EXjV7WV1WhilIiYiISKZIMpJ4Zs0zzNg7AzebG3Paz6FnzZ5Wl3VXFKRERETE6ZKMJPqv7s+sfbNws7kxt8Ncetzfw+qy7pqClIiIiDhVYlIi/df0Z/a+2bjZ3Jj/xHy61ehmdVkOoSAlIiIiTpOYlEjf1X2Z89Mc3G3uzH9iPl1rdLW6LIdRkBIRERGnSExK5KlVTzH357m429xZ0HEBXap3sbosh1KQEhEREYdLTEokeGUw8/fPx93mzsKOC+lcvbPVZTmcgpSIiIg4VEJSAsErg1mwfwEebh4s6riIjtU6Wl2WUyhIiYiIiMMkJCXQZ0UfFv6yEA83DxZ3WswTVZ+wuiynUZASERERh0hISqDX8l4s/nUxHm4eLOm8hPZV2ltdllMpSImIiMhdS0hKoOfynnz161d4unmypPMS2lVpZ3VZTqcgJSIiInfFnmin5/KeLPltCZ5unizrsow2ldtYXVamUJASERGRDLMn2um+rDvLDizDy92LZV2W0bpSa6vLyjQKUiIiIpIh9kQ73ZZ1Y/mB5Xi5e7G8y3JaVWpldVmZSkFKRERE0i0+MZ5uS7ux4uAKvN29WdF1BS0qtrC6rEynICUiIiLpEp8YT5clXVh1aBXe7t6s7LaS5vc1t7osSyhIiYiISJrFJcTReUln1vy+Bm93b1Z1W0XQfUFWl2UZBSkRERFJk7iEODot6cTa39fi4+HDqm6rCLw30OqyLKUgJSIiIncUlxBHx686su7wOnw8fFjdbTXN7m1mdVmWU5ASERGR24pNiKXjVx1Zf3g9uTxysab7GppUaGJ1WS5BQUpERERuKTYhlg6LO7Dxj43k8sjF2h5raVy+sdVluQwFKREREUlVbEIs7Re1Z9ORTeTyyMW6HusIKB9gdVkuRUFKREREbnLdfp32i9sTeiQUX09f1vVYh385f6vLcjkKUiIiIpLCdft12i1qR9ifYfh6+rK+x3oalWtkdVkuSUFKREREksXYY2i3qB2b/9xMbs/crO+5nsfvedzqslyWgpSIiIgAZohqs7ANW49uJbdnbjb03EDDexpaXZZLU5ASERERouOjabOwDeHHwvHz8mNDzw08VvYxq8tyeQpSIiIiOVx0fDStF7Ym4lgEebzysLHXRhqUaWB1WVmCgpSIiEgOdi3+Gq0XtGbb8W3k8crDpl6bqF+mvtVlZRkKUiIiIjnUtfhrtJzfkh0ndpDXOy+bem3ikdKPWF1WlqIgJSIikgNdjbtKywUt+frE1+T1zktor1AeLv2w1WVlOQpSIiIiOczVuKu0mN+Cb05+Qz7vfIT2DuWhUg9ZXVaWpCAlIiKSg0TFRdFifgt2ntxJPu98hPUO48FSD1pdVpalICUiIpJDRMVF0Xxec3b9tYv8PvkJ6x1GvZL1rC4rS1OQEhERyQGuxF6h+fzmfPvXtxTwKcDmPpupU6KO1WVleQpSIiIi2dyV2CsEzQviu1PfKUQ5mIKUiIhINnY59jJB84L4/tT3FMxVkM29N1O7RG2ry8o2FKRERESyqcuxlwmcG8gPp3+gUK5CbOmzhQeKP2B1WdmKgpSIiEg2dOn6JQLnBbL79G4K+xZmS58t1CxW0+qysh0FKRERkWzm4vWLNJvbjB/P/Ehh38Js7bOV+4vdb3VZ2ZKClIiISDZy8fpFms5pyt6zeyniW4StwVupUbSG1WVlWwpSIiIi2cTfMX/TdG5T9p3dR9HcRdnaZyvVi1a3uqxsTUFKREQkG4iMiaTpnKb8dO4nhahMpCAlIiKSxUXGRNJkThN+PvczxXIXIzw4nKpFqlpdVo6gICUiIpKFXYi+QJM5Tdh/fj/F/YoTHhxOlcJVrC4rx3CzugARERHJmPPR52k8pzH7z++nhF8JIoIjFKIymXqkREREsqDz0edpHNKYXy/8Sgm/EoQHh1O5cGWry8pxFKRERESymHPXztF4TmN+u/AbJfOUJDw4nEqFKlldVo6kICUiIpKFnL12lsYhjTkQeYBSeUoRHhxOxUIVrS4rx1KQEhERyQKSkuC3Y+d4YnFHDl89Tsm8FVnfeQMlfe4lOtrq6jLPv7+rYVhXxw0KUiIiIlnAr8fOUfPeYsA3AJwGHhhlaUmWi4lKoEABT0tr0F17IiIiLu701dO0X9TO6jJcj81mdQXqkRIREXFlp6+eJiAkgD+v/ZW87tw5yJ3bwqKscO0aNGuGsf9noivXYfPQoRQu1tbqqhSkREREXNWpqFMEhARw+OJhyuSrwsn/rc+dO4cFqaQk6NkL9n8LRYrgvWYmfr/9hpsLXFdzgRJERETkv/6K+gv/EH8OXzzMPfnuYWOvjVaXZJ1Ro2DVKvD2hpUroVw5qytKph4pERERF3PyykkCQgI4cukI5fKXIyI4gsKe91hdljVmzYL33jPfz5wJDRqA3W5tTf+iHikREREXcuLKCfxD/Dly6Qjl85cnIjiCe/Ln0BC1bRs8+6z5/v/+D3r0sLaeVKhHSkRExEUcv3ycgJAAjl4+SoUCFQgPDqdsvrJWl2WN33+HDh3M3qcuXWDcOKsrSpV6pERERFzAscvH8A/x5+jlo9xb4F4igiNyboj6+29o1QouXYKHH4bZs3GJkeWpUI+UiIiIxY5dPob/bH+OXzluhqgnIyidt7TVZVkjLs7sifrjD7jnHnOQea5cVld1SwpSIiIiFjp66Sj+If6cuHKC+wreR0RwBKXylrK6LGsYBjzzDOzYAXnzwrp1UKyY1VXdlmv2k4mIiOQAf176MzlEVSpUKWeHKIC334Y5c8DdHb76CqpXt7qiO1KPlIiIiAWOXDxCQEgAJ6NOUqlQJcKDwymZp6TVZVln8WIYM8Z8/8knEBRkbT1plK4eqQkTJvDggw+SJ08eihYtSvv27Tl06NBtPxMREYHNZrvpdfDgwbsqXEREJKv64+If+If4czLqJJULVSYiOCJnh6hvvoHgYPP9sGHw3HPW1pMO6QpS27ZtY9CgQXz77beEhYWRkJBAYGAg0dHRd/zsoUOHOHPmTPKrYsWKGS5aREQkq/rj4h/4z/bnr6i/qFK4ChFPRlAiTwmry7LOH39Au3bmIPN27eD9962uKF3SdWlv48aU09PPmjWLokWLsmfPHh5//PHbfrZo0aLkz58/3QWKiIhkF6fjTjNw3kBOXztN1cJV2Rq8leJ+xa0uyzoXL5rTHPz9N9SrB/Pnm+OjspC7GiN15coVAAoWLHjHbWvXrk1sbCzVqlVjzJgxBAQE3HLbuLg44uLikpejoqIAsNvt2J00LfyN/Tpr/zmF2tEx1I6OoXZ0DLWjY/x27jfG/DGGi/aLVC1cldAeoRTyLpTmdjU38/zfe7srPSUlY+LicG/fHrfff8coW5aE5cvByytNj39x9jmZnv3aDMMwMnIQwzBo164dly5dYseOHbfc7tChQ2zfvp26desSFxfH3LlzmTZtGhEREbfsxRo3bhzjx4+/af2CBQvw9fXNSLkiIiKWORV7ijF/jOFSwiXK+pTl9XtfJ79n/nTtIzbWnW7dWgOwaNFafHwSnVBpJjEM6kyeTJmICOy+vuyYMIGr97jOY3BiYmLo0aMHV65cIW/evLfdNsNBatCgQaxbt46vv/6a0qXTN2lYmzZtsNlsrF69OtXfp9YjVaZMGSIjI+/4hTLKbrcTFhZGs2bN8PT0dMoxcgK1o2OoHR1D7egYase7czDyIIHzAzkbfZayPmXZ3m87JfOlf2B5dDQUKGC2/6VLdnLndnSlmcft9ddxf/NNDHd3ElevxmjWLF2fd/Y5GRUVReHChdMUpDJ0ae/5559n9erVbN++Pd0hCuCRRx5h3rx5t/y9t7c33t7eN6339PR0+l/izDhGTqB2dAy1o2OoHR1D7Zh+By4cIHCBGaJqFKnBS8VeomS+khlqx39/xPyzcGChmWn2bHjzTQBsU6fi0bJlhnflrHMyPftM1117hmEwePBgli9fztatWylfvny6iwPYu3cvJUrk4DsUREQk2/vtwm8EhARw9tpZaharSWjPUPJ55LO6LGtt3gxPP22+HzXqn/dZWLp6pAYNGsSCBQtYtWoVefLk4ezZswDky5ePXP97Ds6oUaM4deoUc+bMAWDSpEmUK1eO6tWrEx8fz7x581i2bBnLli1z8FcRERFxDTdC1Pno8zxQ7AG29NlCXk/nDE3JMn75BTp2hIQE6N49uVcqq0tXkJo6dSoA/v7+KdbPmjWLJ598EoAzZ85w4sSJ5N/Fx8czYsQITp06Ra5cuahevTrr1q2j5V105YmIiLiqX87/QuOQxlyIuUCt4rXY3HszhXzTfndetnT6NLRsCVFR0LAhzJoFbtnjKXXpClJpGZc+e/bsFMsjR45k5MiR6SpKREQkK/p3iKpdvDab+2ymYK47TxGUrV27Bq1bw8mTULkyrFwJqYyDzqqyRxwUERGx2P5z+wkICeBCzAXqlKijEAXmZbwuXWDvXihSBNavhzTMPZmVKEiJiIjcpZ/O/kRASACRMZHULVGXzb0VojAM85l5GzZArlywZg1UqGB1VQ6nICUiInIXfjr7E03mNOHv639Tr2Q9wnqHUSBXAavLst5bb8GXX5pjoRYtgocftroip7irR8SIiIjkZPvO7qPJnCZcvH6RB0s+SGjvUPL75Le6LOvNmQP/93/m+08+gbZtra3HiRSkREREMmDvmb00mdOES7GXeLjUw2zqtYl8Pjl8nigw54rq1898P3IkDBxobT1Opkt7IiIi6fTjmR+TQ9QjpR9RiLrh55//mSuqWzeYMMHqipxOPVIiIiLpsOf0HprObcrl2MvUL12fjb02ktc7h0+2CXDiBLRoYc4V1aiR+SiYbDJX1O1k/28oIiLiILtP704OUQ3KNFCIuuHSJWje3Jx4s3p1WLEiW80VdTvqkRIREUmDH079QLO5zbgSd4VHyzzKhp4byOOdx+qyrBcbC+3awYEDUKqUOd1BgZxz16J6pERERO7g+1Pf03RuU67EXeGxso8pRN2QlAS9e8OOHZA3rxmiypSxuqpMpSAlIiJyG9/99R3N5jYjKi6KhmUbKkTdYBgwfDgsXQqenuajX+6/3+qqMp2ClIiIyC3sOrkrOUQ9fs/jrO+5Hj8vP6vLcg0TJ8Lkyeb7OXMgIMDaeiyiICUiIpKKnSd3EjQviKvxV/Ev58/6HgpRyebNM+eIAnj/fXOqgxxKQUpEROQ/vjnxTXKICigXwNrua8ntldvqslxDaCg89ZT5fvhwGDHC2nosprv2RERE/uXrE1/TfF5zou3RNC7fmDXd1+Dr6Wt1Wa5hzx544glzws3u3c3eqBxOPVIiIiL/s/349uQQ1aR8E4WofztyBFq2hOhoaNIkx0y4eSdqAREREWDbsW20nN+SaHs0TSs0ZXX31QpRN5w/D0FB5s9atWD5cvDysroql6AgJSIiOV7EsQhaLjBDVLMKzVjdTSEq2dWr5qNfjhyBcuXMuaLyajb3GxSkREQkRws/Gk6rBa2IsccQdG8Qq7qtIpdnLqvLcg1xcdChA/z4IxQpYg40L17c6qpcigabi4hIjrX16FZaL2jN9YTrNL+vOSu6rsDHw8fqslxDUhL06QNbtoCfn9kTVbGi1VW5HPVIiYhIjrTlzy20WtCK6wnXaVmxpULUvxkGvPACfPWVOWv58uVQt67VVbkkBSkREclxNv+5mdYLWxObEEuriq1Y3mW5QtS/vf02fPqp+X7OHGjWzNp6XJiClIiI5CihR0Jps7ANsQmxtK7UmmVdluHt4W11Wa5j+nQYM8Z8P3lyjp61PC0UpEREJMfY9Mcm2i5sS2xCLG0rt2Vp56UKUf+2bBkMGGC+HzUKhgyxtp4sQEFKRERyhI1/bKTdonbEJcbRrnI7lnReohD1b1u3Qo8e5iDzp5+Gt96yuqIsQUFKRESyvQ2HNySHqPZV2vNV56/wcteEksl274Z27SA+3nwEzNSpYLNZXVWWoCAlIiLZ2vrD62m/uD3xifF0qNKBxZ0WK0T926FD5oSb165BQADMnw/u7lZXlWUoSImISLa19ve1dFjcgfjEeDpW7agQ9V9//QWBgRAZCXXqwMqV4KO7F9NDE3KKiEi2tObQGjp+1RF7kp1O1Tqx4IkFeLp7Wl2W64iMNEPUiRPmRJt69EuGqEdKRESyndWHVieHqC7VuyhE/deN5+cdOAClS0NYGBQtanVVWZKClIiIZCsrD66k01edsCfZ6Vq9K/OfmK8Q9W+xsdC+vTnAvFAh8/l599xjdVVZloKUiIhkGysOrKDzks7Yk+x0q9GNeU/Mw8NNo1iSJSRA9+7mVAd+frBxI1StanVVWZqClIiIZAvLDyyny9IuJCQl0OP+HsztMFch6t+SkuCZZ8wB5d7esHo11KtndVVZnoKUiIhkeUt/W0qXJWaI6nl/T+a0n6MQ9W+GAS++CLNmgZsbLFpkTnUgd01BSkREsrQlvy6h29JuJBqJ9K7Zm5D2Ibi7aR6kFN54AyZNMt/PnGmOkRKHUJASEZEsa/Evi+m+rDuJRiJ9HujDrHazFKL+a/JkGDv2n/fBwdbWk80oSImISJa06JdF9Fzek0QjkSdrPcnMtjMVov5r9mwYOtR8//rregixEyhIiYhIlrNg/4LkEPVUraf4ss2XClH/tXw59Otnvh8+HMaMsbaebEpBSkREspT5P8+n94reJBlJ9Kvdjy/bKkTdZNMm6NbNvFOvXz+YOFEPIXYSBSkREcky5v08jz4r+5BkJNG/dn++aPMFbjb9U5bC9u3QoQPY7dCpE3z+uUKUE+nsExGRLGHOT3Pos8IMUU/XeZrP23yuEPVfP/wArVvD9evQsiXMnw/u6q1zJp2BIiLi8kL2hfDkyicxMHi27rNMaz1NIeq/fvkFmjc3n6Pn7w9Ll4KXl9VVZXs6C0VExKXN3jebp1Y9hYHBc/WeY0qrKQpR/3X4MDRtChcvwsMPm7OW58pldVU5gs5EERFxWTP3zqTvqr4YGAysN5DPWn6mEPVfx4+bIercOXjgAdiwAfLksbqqHENno4iIuKQZP86g/+r+GBgMfnAwn7b8FJsGTad0+jQ0aQInTkDlyhAaCgUKWF1VjqIgJSIiLmf6nun0X2OGqOcfep6PW3ysEPVfFy6YPVFHjkD58rB5MxQtanVVOY6ClIiIuJQv9nzBM2ufAWDIQ0OY3HyyQtR/XboEzZrBgQNQujRs2WL+lEynICUiIi7j892f8+zaZwEY+vBQJjWfpBCVmvbt4aefoFgxM0SVL291RTmWh9UFiIhIzpaUBJGRMGvvLF7ZNhxsvgx+6HneeGwCMTHZJ0TZ7RAb6050NHh6pv/z0dH/vDf27IZChczLeZUqOa5ISTcFKRERsVRkpNmxAk/97wWf/u+VvXgCrR2yp5g8xfELXQI1ajhkf5JxurQnIiKW+vLHL60uIetZtBjq1LG6CkE9UiIiYqFPvvuEV7e/AvQH4OxZAz+/7HM579/sdjubNm0iKCgIz/Rc24uPh169MNavI8anMCxeROHm9Z1XqKSLgpSIiFhi8reTGbppKNh8k9f5+dnIndu6mpzJbgcfn0Ry507HGKmEBHiyJ6xfCj4++K2bBY0VolyJLu2JiEim+2jXR2aIAkbUf8naYlxVYiI8+eQ/z8xbsQIaN7a6KvkPBSkREclUH+36iOGhwwF4teGrjPUfa3FFLigxEfr2hfnzwcMDliwxH0gsLkdBSkREMs0HOz9IDlH/9/j/8UbAG5on6r+SkuCZZ2DOHHB3h0WLoG1bq6uSW1CQEhGRTPH+N+8zImwEYIao8f7jFaL+KykJnnsOZs4ENzezR6pjR6urkttQkBIREad79+t3Gbl5JADjGo3j9YDXFaL+yzDg+efhiy/MEDV3LnTtanVVcgcKUiIi4lQTdkzglS2vADDef7zGRKXGMGDYMJgyBWw2mDULevSwuipJA01/ICIiTvP2jrd5deurALwR8AZjHh9jcUUuyDBg+HCYPNlc/vJL6NPH2pokzRSkRETEKd7c/ib/F/5/ALzV+C1GNxxtcUUuyDBgxAiYNMlc/uIL8249yTIUpERExOFe3/Y6YyPMS3gTmkzglcdesbgiF2QY8NJL8OGH5vLnn8PTT1tbk6SbgpSIiDjUuIhxjN82HoB3mrzDy4+9bHFFLsgw4OWX4YMPzOVp08wpDyTLUZASERGHMAyDcRHjeH376wC81/Q9XnpUs5bfxDBg1Ch4/31zecoUePZZa2uSDFOQEhGRu2YYBmMjxvLG9jcAeL/Z+4xoMMLiqlyQYeA2evQ/PVGffmrOGyVZloKUiIjcFcMweC38Nd7c8SYAHwR+wPD6wy2uygUZBtVCQnBfudJc/uQTGDTI0pLk7ilIiYhIhhmGwZitY3j767cB+DDwQ4bVH2ZxVS7IMHB75RUq3ghRn30GAwdaWpI4hoKUiIhkiGEYjN4ymne+eQeASUGTeOGRFyyuygUZBrz4Iu4ffQRA4qef4q4QlW1oZnMREUk3wzB4ZfMrySFqcvPJClGpuTHZ5v9C1L7nniNJd+dlK+qREhGRdDEMg5FhI5m4ayIAn7T4hMEPDba4KhdkGDBkiDmgHEiYOpXjJUpQ3eKyxLHUIyUiImlmGAYvhb2UHKI+bfGpQlRqkpLMu/E+/dR8dt6XX2L062d1VeIE6QpSEyZM4MEHHyRPnjwULVqU9u3bc+jQoTt+btu2bdStWxcfHx8qVKjAtGnTMlywiIhYwzAMXgx9kQ92mbfuT2k5hUEP6a6zmyQlmZNrfv75Pw8gVojKttIVpLZt28agQYP49ttvCQsLIyEhgcDAQKKjo2/5maNHj9KyZUsaNmzI3r17GT16NEOGDGHZsmV3XbyIiGQOwzB4afNLfPStOdZnaqupPPeg5j+6SWIiPPUUzJgBbm4wbx4EB1tdlThRusZIbdy4McXyrFmzKFq0KHv27OHxxx9P9TPTpk2jbNmyTPrfAxmrVq3K7t27mThxIh07dsxY1SIikmkMw2DGqRmsjVwLwOetP+eZuhowfZOEBHjySZg/H9zdYcEC6NLF6qrEye5qsPmVK1cAKFiw4C232bVrF4GBgSnWBQUFMWPGDOx2O56enjd9Ji4ujri4uOTlqKgoAOx2O3a7/W5KvqUb+3XW/nMKtaNjqB0dQ+149wzDYOimockhamqLqTxV8ymHtqm5K8//vbeTJf+47Hbce/fGbflyDA8PEufNw+jQgX9/GZ2PjuPstkzPfm2GYRgZOYhhGLRr145Lly6xY8eOW25XqVIlnnzySUaPHp28bufOnTz66KOcPn2aEiVK3PSZcePGMX78+JvWL1iwAF9f34yUKyIi6WQYBtNPTWd95Hps2BhYZiDNCjVz+HFiY93p1q01AIsWrcXHJ9Hhx3AmN7udeu+/T4nvvyfRw4PdI0dy9qGHrC5L7kJMTAw9evTgypUr5M2b97bbZrhHavDgwfz88898/fXXd9zWZrOlWL6R3f67/oZRo0YxfPg/jxeIioqiTJkyBAYG3vELZZTdbicsLIxmzZql2ksmaaN2dAy1o2OoHTPOMAxe2PRCcogaVGYQ73Z71ynt+O9htkFBQeTO7fBDOM/167h37ozb999j+PhgLFlCnaCgVDfV+eg4zm7LG1fC0iJDQer5559n9erVbN++ndKlS9922+LFi3P27NkU686fP4+HhweFChVK9TPe3t54e3vftN7T09PpJ19mHCMnUDs6htrRMdSO6ZNkJDF4/WCm/TgNGzamt55O4b8KO60d/71L8xgOP4RzREdD+/YQHg6+vthWr8ajSZM7fkzno+M475xM+z7TddeeYRgMHjyY5cuXs3XrVsqXL3/Hz9SvX5+wsLAU60JDQ6lXr55OJBERF5NkJDFw3UCm7p6KDRuz2s2iT80+Vpfleq5cgebNzRDl5wcbN0IaQpRkP+kKUoMGDWLevHksWLCAPHnycPbsWc6ePcv169eTtxk1ahR9+vzzl27AgAEcP36c4cOHc+DAAWbOnMmMGTMYMWKE476FiIjctSQjiQFrB/D5ns+xYSOkfQjBtXTr/k0uXoSmTeHrryFfPggLg4YNra5KLJKuIDV16lSuXLmCv78/JUqUSH4tXrw4eZszZ85w4sSJ5OXy5cuzfv16IiIiqFWrFm+88QYff/yxpj4QEXEhSUYSz655luk/TsfN5sacDnPo/UBvq8tyPefOgb8/7N4NhQrB1q3wyCNWVyUWStcYqbTc4Dd79uyb1jVq1Igff/wxPYcSEZFMkmQk8fTqp5m5byZuNjfmdphLj/t7WF2W6/nrL7Mn6tAhKF7c7ImqUcPqqsRiemixiEgOlmQk0X91f2btm4WbzY15HebR/f7uVpfleo4eNcdAHT0KZcrAli1QsaLVVYkLUJASEcmhEpMS6b+mP7P3zcbN5sb8J+bTrUY3q8tyPQcPmj1Rp07BvfeaIeqee6yuSlxEusZIiYhI9pCYlEjf1X2ZvW827jZ3FjyxQCEqNXv3wuOPmyGqalXYvl0hSlJQkBIRyWESkxJ5atVTzPlpjhmiOi6ga42uVpflenbtgoAAuHAB6tQxQ1TJklZXJS5GQUpEJAdJTEokeGUwc3+ei7vNnUWdFtGluh6se5MtW6BZM3O+qMceM+/OK1zY6qrEBSlIiYjkEAlJCfRZ2Yf5++fj4ebB4k6L6VStk9VluZ7Vq6FlS3Pm8sBA2LTJnC9KJBUKUiIiOUBCUgK9V/Rmwf4FySGqYzXN53eTefPgiScgPt78uXo1+PpaXZW4MAUpEZFsLiEpgV7Le7Hol0V4uHnwVaeveKLqE1aX5Xo+/RR694bEROjTBxYvhlSe+yrybwpSIiLZWEJSAj2X92Txr4vxdPNkSecldKjaweqyXIthwJtvwvPPm8tDhsCsWeChGYLkznSWiIhkU/ZEOz2X92TJb0vwdPNkaZeltK3c1uqyXIthwIgR8OGH5vLYsebLZrO2LskyFKRERLIhe6Kd7su6s+zAMrzcvVjWZRmtK7W2uizXkpAAzz4LM2eay5MmwQsvWFqSZD0KUiIi2Yw90U63Zd1YfmA5Xu5eLO+ynFaVWlldlmuJjYUePWDFCnBzgxkz4Mknra5KsiAFKRGRbCQ+MZ5uS7ux4uAKvNy9WNF1BS0rtrS6LNcSFQXt20N4uDmYfOFC6KBxY5IxClIiItlEfGI8XZZ0YdWhVXi7e7Oi6wpaVGxhdVmu5fx5aNECfvwR8uSBVavM2ctFMkhBSkQkG4hPjKfzks6sPrQab3dvVnVbRdB9QVaX5VqOHzcn2Pz9dyhSBDZuNB/9InIXFKRERLK4uIQ4Oi/pzJrf1+Dj4cOqbqsIvDfQ6rJcy6+/QlCQ+fDhsmUhLAwqVbK6KskGNI+UiEgWFpcQR8evOiaHqNXdVitE/dc335jPyzt1CqpVM5cVosRBFKRERLKo2IRYnvjqCdYdXkcuj1ys7b6WZvc2s7os17J2LTRtCpcvQ4MGsGMHlC5tdVWSjShIiYhkQbEJsTyx+AnWH15PLo9crOm+hiYVmlhdlmuZPdu8Oy82Flq1Mi/nFSxodVWSzShIiYhkMbEJsbRf1J4Nf2wgl0cu1vVYpxD1b4YB774LTz1lPjcvONicL0oPHxYnUJASEclCrtuv025ROzYd2YSvpy/re64noLxu30+WlATDhsErr5jLL71kPjfP09PauiTb0l17IiJZxI0QFfZnmBmieqynUblGVpflOuLioE8f+Oorc/mDD2D4cGtrkmxPQUpEJAuIscfQblE7Nv+5mdyeuVnfcz2P3/O41WW5jitXzPFQERFm71NICHTvbnVVkgMoSImIuLgYewxtFrZh69Gt5PbMzYaeG2h4T0Ory3Idp0+bs5X//LM5W/mKFdBEY8YkcyhIiYi4sOj4aNosbEP4sXD8vPzY0HMDj5V9zOqyXMeBA9C8OZw4AcWKwYYNULu21VVJDqLB5iIiLio6PprWC1sTfiycPF552NRrk0LUv339NTz6qBmiKlaEXbsUoiTTKUiJiLig6PhoWi1oRcSxiOQQ1aBMA6vLch1Ll5oTbV66BPXrw86dUL681VVJDqQgJSLiYq7FX6PlgpZsO76NvN55Ce0dSv0y9a0uy3VMmgRduph36bVvD5s3Q+HCVlclOZSClIiIC7kad5UW81uw/fh2M0T1CuWR0o9YXZZrSEqCF18054kyDBg0yOyZ0kSbYiENNhcRcRE3QtQ3J78hn3c+QnuH8lCph6wuyzVcv27OEbV0qbn8zjswciTYbNbWJTmegpSIiAuIiouixfwW7Dy5k3ze+QjrHcaDpR60uizXEBkJ7dqZ46C8vMyZynv0sLoqEUBBSkTEclFxUTSf15xdf+0iv09+wnqHUa9kPavLcg1//GHOEfXHH5A/P6xcCY00m7u4DgUpERELXYm9QtC8IL479R0FfAqwuc9m6pSoY3VZruHbb6FNG7NH6p57zDmiqla1uiqRFDTYXETEIpdjLxM4L1AhKjVLlkBAgBmi6tY1Q5VClLggBSkREQtcjr1M4NxAvj/1PQVzFWRLny0KUWDejffee+b0BrGx0Lq1+fy84sWtrkwkVQpSIiKZ7NL1SzSb24wfTv9AoVyF2NpnK7VLaEZuAIYMgZdfNt8//7w5JsrPz9KSRG5HY6RERDJJUhL8cfISnZZ0Zv/F3yjoW4a1ndZxX577iY62urpbs9shNtad6Gjw9HT8/v/93Y1ZM8HNDT76yAxVIi5OQUpEJJMcPnmRKuUKApsBuAjU/z9LS0ojT6B1phwpxqcwfl99ag4yF8kCdGlPRCQTXLx+kU5fdbK6DNe3erVClGQp6pESEXGyv2P+puncpvxy6ffkdefOQe7cFhaVDna7nU2bNhEUFISnI6/tLVsGzzyDERdLTLUHYf4CCtd8wHH7F8kEClIiIk50I0TtO7uPIn7luPC/9blzZ6UgBT4+ieTO7aAxUoYBb70F//e/65qtW+O3cKEGlUuWpEt7IiJOEhkTSZM5Tdh3dh/FchdjfY/1Vpdkvbg4CA7+J0QNG6Y78yRLU4+UiIgTXIi+QJM5Tdh/fj/FchcjPDicsr45fELJ8+ehQwfzmXnu7vDppzBggNVVidwVBSkREQf7d4gq7lec8OBwqhSu4tJTHDjd/v3mIPLjx81n5i1ZAk2bWl2VyF3TpT0REQc6H32exnMas//8fkr4lSAiOIIqhatYXZa11q6FBg3MEFWxovm4F4UoySYUpEREHOTctXMEhATwy/lfKJmnJBFPRlC5cGWry7KOYcAHH0DbtnDtmvnsvG+/hco5uE0k21GQEhFxgHPXztF4TmN+u/CbGaKCI6hUqJLVZVknLg769oURI8xA9fTTsGkTFCxodWUiDqUxUiIid+nstbMEhARwMPIgpfKUIjw4nIqFKlpdlnXOnoUnnoBdu8zHvXz4ofm4F5vN6spEHE5BSkTkLpy5eobGcxpzMPIgpfOWJjw4nPsK3md1WdbZu9e8lPfXX+ag8q++gmbNrK5KxGl0aU9EJINOXz2Nf4g/ByMPUiZvGSKCI3J2iFqyBB591AxRlSvDd98pREm2pyAlIpIBp6+eJiAkgN///p2y+coS8WQE9xa81+qyrJGUZE6w2aULXL8OQUHmoPJKOXiMmOQYurQnIpJOp6JOERASwOGLh7kn3z2EB4dTvkB5q8uyRlQU9OoFa9aYy8OHw7vvgof+eZGcQWe6iEg6/BX1FwEhAfxx8Q/K5S9HeHA45fKXs7osaxw+DO3awYED4O0N06dD795WVyWSqRSkRETS6OSVkwSEBHDk0hHK5S9HRHAE9+S/x+qyrBEaCl27wuXLULKk+by8Bx+0uiqRTKcxUiIiaXDiygn8Q/w5cukI5fOXZ9uT23JmiDIMeO89aNHCDFH168Pu3QpRkmMpSImI3MHxy8fxn+3Pn5f+pEKBCkQ8GUHZfGWtLivzRUdDt27w8svmAPN+/SA8HEqUsLoyEcvo0p6IyG0cv3wc/xB/jl0+xr0F7iU8OJwy+cpYXVam8z17Fo+GDeGXX8yB5B9/DAMGaJJNyfEUpEREbuHY5WMEhARw7PIx7it4H+HB4ZTOW9rqsjKdLSyMRiNGYLt2DYoVg6VL4bHHrC5LxCXo0p6ISCqOXjqK/2yzJ6piwYpEBEfkvBBlGDBhAu6tW+N17RpJDz5ojodSiBJJph4pEZH/+PPSnwSEBHDiygkqFarE1j5bKZW3lNVlZa6oKHjySVixAhtwvGlTSi5fjluePFZXJuJSFKRERP7lz0t/4j/bn5NRJ6lUqBLhweGUzFPS6rIy18GD0KGD+dPLi4TJk9lXogQlfXysrkzE5ejSnojI/xy5eIRGsxtxMuoklQtVJiI4IueFqOXLzakMDh6EUqVg+3aMfv2srkrEZSlIiYgAf1z8g0azG/FX1F9UKVyFiCcjKJEnB93Wn5AAI0dCx45w7Ro0agR79sDDD1tdmYhLU5ASkRzv8N+H8Z/tz6mrp6hauCrhweEU9ytudVmZ5+xZaNoU3n/fXH7xRdi82bxDT0RuS2OkRCRH+/3v3wkICeD01dNUK1KNrX22UswvBwWIb76Bzp3hzBnw84NZs6BTJ6urEsky1CMlIjnWochD+M/25/TV01QvUp3w4PCcE6IMAyZNAn9/M0RVrQo//KAQJZJO6pESkRzpUOQhAkICOHPtDDWK1mBLny0UzV3U6rIyR1QU9O0Ly5aZy127wpdfmj1SIpIu6pESkRznYORB/EP8OXPtDPcXvZ+tfbbmnBD1889Qr54Zojw9YfJkWLhQIUokg9QjJSI5yoELBwgICeBc9DlqFqvJlj5bKOxb2OqyMsesWTBwIMTGQpkysGSJ7soTuUvqkRKRHOO3C7/hH+LPuehzPFDsgZwTomJizEt5ffuaIap5c9i7VyFKxAHSHaS2b99OmzZtKFmyJDabjZUrV952+4iICGw2202vgwcPZrRmEZF0++X8L/jP9ud89HlqFa+Vc0LUwYNmYJo1C2w2eOMNWLcOChWyujKRbCHdl/aio6N54IEHeOqpp+jYsWOaP3fo0CHy5s2bvFykSJH0HlpEJEN+Of8LQQuCuBBzgdrFa7O5z2YK5ipodVnON38+PPssREebc0ItWACNG1tdlUi2ku4g1aJFC1q0aJHuAxUtWpT8+fOn+3MiInfj2PVj9J/fn8jrkdQpUYew3mHZP0Rdvw4vvADTp5vLjRuboap4DppkVCSTZNoYqdq1a1OiRAmaNGlCeHh4Zh1WRHKwn8//zP/98X9EXo+kbom6OSNE3biUN326eSlv7FgIDVWIEnESp9+1V6JECb744gvq1q1LXFwcc+fOpUmTJkRERPD444+n+pm4uDji4uKSl6OiogCw2+3Y7Xan1Hljv87af06hdnQMtePd++ncTzRf0JyriVepU7wO67utJ49HHkvb1Dy05//e23F0KbY5c3AfMgRbTAxG0aIkhoRgNGkCSUnmK4N0PjqG2tFxnN2W6dmvzTAMI6MHstlsrFixgvbt26frc23atMFms7F69epUfz9u3DjGjx9/0/oFCxbg6+ubkVJFJAf5M+ZPxh4Zy9XEq1T0rcjYCmPx87B+nqTYWHe6dWsNwKJFa/HxSXTIft2vX+eBzz+nTEQEABdq1mTPsGHEFSjgkP2L5DQxMTH06NGDK1eupBjfnRpLgtRbb73FvHnzOHDgQKq/T61HqkyZMkRGRt7xC2WU3W4nLCyMZs2a4enp6ZRj5ARqR8dQO2bc3rN7abGwBRevX+TBEg8ytPBQ2jdv7xLtGB0NBQqYdVy6ZCd3bgfs9Kef8OjRA9vhwxhubiSNHUvSyJHg7u6AnZt0PjqG2tFxnN2WUVFRFC5cOE1BypIJOffu3UuJEiVu+Xtvb2+8vb1vWu/p6en0ky8zjpETqB0dQ+2YPj+e+ZHmC5pzKfYSj5R+hDVd1vDN1m9cph3/XYJZ013szDDgk0/gpZcgPh5KlcK2cCHuDRviuAiVkqu0Y1andnQcZ7VlevaZ7iB17do1/vjjj+Tlo0ePsm/fPgoWLEjZsmUZNWoUp06dYs6cOQBMmjSJcuXKUb16deLj45k3bx7Lli1j2Y1nPImIOMCe03toOrcpl2MvU790fTb22kgut1xWl+UckZHm5Jpr1pjLbdrAzJlQOAfMiyXiYtIdpHbv3k1AQEDy8vDhwwEIDg5m9uzZnDlzhhMnTiT/Pj4+nhEjRnDq1Cly5cpF9erVWbduHS1btnRA+SIi8MOpHwicF8jl2Ms0KNOADT03kNc7b/Yc1BseDr16wenT4OUFEyfC4MHmHXoikunSHaT8/f253bCq2bNnp1geOXIkI0eOTHdhIiJp8f2p7wmcG8iVuCs8WuZRNvTcQB7vPFaX5Xh2O4wfD2+/bV7Wq1wZFi+GBx6wujKRHE0PLRaRLOu7v74jcF4gUXFRPFb2Mdb3WJ89Q9SRI9CzJ3z3nbncty98/DGOGa0uIndDDy0WkSzp27++TQ5RDcs2zJ49UYYBc+dCrVpmiMqXz+yFmjFDIUrERahHSkSynF0ndxE0L4ir8Vd5/J7HWddjHX5e1s8T5VBXrsBzz8HCheZyw4Ywbx6ULWttXSKSgnqkRCRL2XlyZ3KI8i/nz/oe67NfiNq+HWrWNEOUuzu8+aY5yFwhSsTlqEdKRLKMb058Q/P5zbkWf42AcgGs6b6G3F7Z6BJXfLz5bLx33zUv61WoYD5s+JFHrK5MRG5BQUpEsoR/h6jG5RuzpvsafD2z0SOjDh40B5T/+KO53LcvTJoEebLZuC+RbEaX9kTE5e04voOgeUFci79Gk/JNsleIMgz47DOoU8cMUQULwrJl5oByhSgRl6ceKRFxaduPb6fl/JZE26NpVqEZq7qtIpdnNpmx/NQps+cpNNRcbtYMZs+GkiUtLUtE0k49UiLisrYd20aL+S2ItkcTeG9g9gpRS5fC/febIcrHx5wXauNGhSiRLEY9UiLicpKSYNWPX9NjeR9igSYV2jK/9SKS4nMRHZ/2/djtEBvrTnQ0d/eAYAeJjv7nvfFkMBADdeua0xpUqWJZXSKScQpSIuJyVu7ZQceHGgLHAdgCFHk6I3vyBFo7rjAHirHlwe//RsCYMa6R8kQkQxSkRMSlbPlzCz2WPwWcuOO2WdratdCyntVViMhdUpASEZex+c/NtFnYhjjbP8M3z53L+NNQ7HY7mzZtIigoCE+ren127IBnn4UTxzGAmKeHwuhXKVxWIUokO1CQEhGXEHYkjLaL2hKbEEvzih3Z+L/1uXPfTZACH59Ecue24OpZdDSMHm0OIge45x6YNQu/gIBMLkREnEl37YmI5Tb9sYk2C9sQmxBL28ptmf/EfKtLujs7dsADD/wTovr1g59/BoUokWxHQUpELLXxj420W9SOuMQ42lVux5LOS/D28La6rIyJiYFhw6BRIzhyBEqXhg0b4MsvIW9eq6sTESfQpT0RscyGwxtov7g98YnxtK/SnsWdFuPl7oXd6sIy4uuvzck1Dx82l/v2hQ8/hHz5rK1LRJxKPVIiYon1h9cnh6gOVTrwVaev8HL3srqs9Lt2DYYMgccfN0NUqVKwfr35iBeFKJFsTz1SIpLp1v6+lo5fdSQ+MZ6OVTuysONCPN2z4FxKW7ZA//5w7Ji53K8fTJwI+fNbWZWIZCIFKRHJVGsOraHjVx2xJ9npVK0TC55YkPVC1JUr8NJLMH26uXzPPeb7Zs2srUtEMp0u7YlIpll9aHVyiOpcrXPWDFGrV0O1av+EqEGDYP9+hSiRHEo9UiKSKVYeXEmXJV2wJ9npUr0L85+Yj4dbFvpP0Llz5lior74yl++7z7wbr1Eja+sSEUupR0pEnG7FgRV0XtIZe5KdbjW6Za0QZRgQEgJVq5ohyt0dXn7ZnBdKIUokx8si/yUTkaxq+YHldF3alYSkBHrc34OQ9iFZJ0QdOQIDBsDmzeZy7drm3Xi1a1tbl4i4DPVIiYjTLP1tKV2WdCEhKYGe9/fMOiHKbod334UaNcwQ5eMD77wD33+vECUiKWSB/6KJSFa05NcldF/WnUQjkV41ezG73Wzc3dytLuvOvvsOnnnGvHQH0LQpTJsG995rbV0i4pLUIyUiDrf4l8XJIap3zd5ZI0RduQLPPw/165shqlAhmDMHQkMVokTkltQjJSIOteiXRfRa3otEI5HgB4KZ0XaGa4cow4AlS2DoUDhzxlzXuzd88AEUKWJpaSLi+hSkRMRhFuxfQO8VvUkykniq1lNMbzPdtUPUn3+a80Bt3GguV6wIU6dCkybW1iUiWYYu7YmIQ8z/eX5yiOpXux9ftv3SdUNUXBy89RZUr26GKC8vGDfOvKSnECUi6aAeKRG5a/N+nkfwymCSjCT61+7P520+x83mov+fFhYGgwfD77+by40bm71QlSpZW5eIZEku+l86Eckq5v40lz4r+pBkJPF0naddN0SdOgXdukFgoBmiiheHBQvM6Q0UokQkg1zwv3YiklWE7AsheGUwBgbP1n2Waa2nuVyIsiUk4PbRR1ClCixeDG5u8MILcPAgdO8ONpvVJYpIFqZLeyKSIbP3zabvqr4YGDxX7zk+bfmp64Wo8HAChg7F/a+/zBWPPGJexqtVy9K6RCT7cK3/6olIljBz78zkEDWw3kA+a/mZa4Wov/6Crl3xCAoiz19/YRQubD7a5ZtvFKJExKHUIyUi6TJz70z6r+6PgcHgBwfzcYuPsbnK5bHYWPjwQ3j7bYiOxnBz42jz5pSZNQvPokWtrk5EsiEFKRFJs+l7pvPM2mcAXCtEGQasWQPDhplzQwE8+igJH33E/tOnKVOggLX1iUi25UJ98SLiyr7Y80VyiHrh4RdcJ0QdOADNm0O7dmaIKlkS5s2DHTt0GU9EnE5BSkTuaNruaTy79lkAhj48lI+CPrI+RF26ZD7WpWZN83l4Xl4wahQcOgQ9e+puPBHJFLq0JyK3NeWHKQxaPwiAYY8M44PAD6wNUQkJ8Pnn8NprcPGiua5tW3NslB4uLCKZTEFKRG7ps+8/Y/CGwQC8WP9F3m/2vrUhKjTUHAf122/mcvXq8NFH0KyZdTWJSI6mS3sikqpPvvskOUSNqD/C2hD122/QsiUEBZnvCxWCKVNg3z6FKBGxlHqkRCRZUhJERsL0PV8wZscrYPNl6MPDGNvgDWJiMi9ERUf/894Y8gKEfAaJieDhYT4n77XXQHfiiYgLUJASkWSRkVCsGMAz/3vBpP+9rBIzcwF+JEKHDvDuu1CxooXViIikpEt7IpJs2g9TrS7hZvc/ANu2wfLlClEi4nLUIyUiAHy460PGfvN/wHMAnD1r4OeXiWOitmyBV1+FX/ZjADElKsKroyn8bCh46P/5RMQ1KUiJCBN3TuSlsJfA5pu8zs/PRu7cmXDwvXvhlVfMO/IA8uWDV1/F7/nnwccnEwoQEck4/W+eSA733jfvmSEKeOXRUZl34CNHoEcPqFPHDFGenubUBkeOwEsvKUSJSJagICWSg7379bu8vPllAMY1GseYRmOcf9Bz58w776pUgYULzXU9esDBg+akmoUKOb8GEREH0aU9kRxqwo4JjN46GoDx/uN5rdFrKaYdcLjLl+GDD8wJNG8cqHlzmDBBz8QTkSxLQUokB3pr+1uMCTd7n94IeIMxjzuxJyomBj75xJy64NIlc92DD5rLAQHOO66ISCZQkBLJYd7c/ib/F/5/ALzV+C1GNxztnAPFxcGXX8Kbb8LZs+a66tXN5Xbt9FBhEckWFKREcpA3tr3BaxGvAfB247cZ1dAJg8vtdpg92wxMJ06Y68qXh9dfh+7dwd3d8ccUEbGIgpRIDjE+Yjzjto0D4J0m7/DyYy879gAJCTB/vhmY/vzTXFeyJIwZA/36gZeXY48nIuICFKREsjnDMBgXMY7Xt78OwHtN3+OlR19y3AESE2HxYjNAHTpkritaFEaNgmefhVy5HHcsEREXoyAlko0ZhsHYiLG8sf0NAN5v9j4jGoxwzM5TC1CFCsHIkTBoEJkzm6eIiLUUpESyKcMweC38Nd7c8SYAHwR+wPD6w+9+x6kFqIIF4cUXzfmh8ua9+2OIiGQRClIi2ZBhGIzZOoa3v34bgA8DP2RY/WF3t1O73RwD9fbbcPiwuU4BSkRyOAUpkWzGMAxGbxnNO9+8A8CkoEm88MgLGd9hXJx5F94778CxY+a6ggVh+HB4/nkFKBHJ0RSkRLIRwzAYtWUU737zLgCTm09myMNDMraz6GiYPh0mToRTp8x1RYvCiBHw3HPg5+egqkVEsi4FKZFsIjHRYMiy8Uz5YQZ4+jIx6AP61RiQrse+/Htbo0pVuHTSXChVyhxE/vTTugtPRORfFKREsgHDMHh+2Timdh0PjANgxAS4m/vzYi5dx69CBXj5ZQgOBm9vR5QqIpKtuFldgIjcHcMwGBE6gqk/THHsjqdOM+/Ke+YZhSgRkVtQj5RIFmYYBsM3DWfSd5PA0zd5/blzaZjG6Ycf4KOPYPVqwDD399AjxAx6CQIDKVy0o/5XS0TkDhSkRLIowzAYtmkYk7+bDMDkFh/zwgTzd7lz3yJIJSXBmjXmAPKvv/5nfZs25iW8Rx9FQ8hFRNJOQUokCzIMgxc2vsAn338CwBetv6BHlX7ccpKD69chJAQ+/PCfOaA8PaFHD3jpJahePVPqFhHJbhSkRLIYwzAYsmEIn/7wKQDT20ynf53+qd+dd+YMTJkC06ZBZKS5Ln9+GDDAnAOqZMlMq1tEJDtSkBLJQgzDYPD6wUzZPQUbNr5s+yV9a/e9ecN9++DzD2HRInNGcoBy5WDYMOjbV3NAiYg4iIKUSBaRkJhE/0WvELLvK/DMzZTWU+laqXdyT1T0lQRu/JU2HnsUiDF/8eijZoBq1w489FdeRMSR9F9VkSwgyUii38KXmdP7feA9AJ6bAM+l2Oqfv84xbnnx69Yehg6FBx/MvEJFRHIYBSkRF5dkJPHc2ueY89Ny4P20fejHH+GBEk6tS0REMjBLzPbt22nTpg0lS5bEZrOxcuXKO35m27Zt1K1bFx8fHypUqMC0adMyUqtIjpKUBGfPJdF77ot8sWse//7revaBIK6R+59Xrce4+vkCzh2P5dw5KHy/QpSISGZId49UdHQ0DzzwAE899RQdO3a84/ZHjx6lZcuWPP3008ybN49vvvmGgQMHUqRIkTR9XiSnunzFg7JlvIGP/vf6h+2nH8ntlQCdO8PAgVC/PthsmgNKRCSTpTtItWjRghYtWqR5+2nTplG2bFkmTZoEQNWqVdm9ezcTJ05UkBJJhWFA1NUkph/4CmiV+kajx8AL3aFo0UytTUREUnL6GKldu3YRGBiYYl1QUBAzZszAbrfj6el502fi4uKIi4tLXo6KigLAbrdjv3Ert4Pd2K+z9p9TqB3v3tWf/qDwg1WBkOR1RyhH4Sa1uNajP0bTpuQrNhC7G/9MbSCp0vnoGGpHx1A7Oo6z2zI9+3V6kDp79izFihVLsa5YsWIkJCQQGRlJiRI3j+WYMGEC48ePv2l9aGgovr6+N613pLCwMKfuP6dQO6aPW3w8Jb79lrJhYeTefwRIObvm7vdfx7tiPiAR9m6ypMasTOejY6gdHUPt6DjOasuYmJg0b5spd+3ZbLYUy4ZhpLr+hlGjRjF8+PDk5aioKMqUKUNgYCB58+Z1So12u52wsDCaNWuWai+ZpI3aMZ327cNtzhzcFizAdvEiAInAivK5Ofl4B5oM/4y8BX0pUqQ7bnqAcLrpfHQMtaNjqB0dx9lteeNKWFo4PUgVL16cs2fPplh3/vx5PDw8KFSoUKqf8fb2xtvb+6b1np6eTj/5MuMYOYHa8Tb+/hsWLIBZs2Dv3uTVkYV9+bR6DHPquPH2kzMoezQXFav6qh0dQOejY6gdHUPt6DjOasv07NPpQap+/fqsWbMmxbrQ0FDq1aunE0lyDrsdNm6EOXNg9WqIjzfXe3qS1LYtEytHMspjG24eHizquIi2Fduy/uh6a2sWEZE7SvfFgmvXrrFv3z727dsHmNMb7Nu3jxMnTgDmZbk+ffokbz9gwACOHz/O8OHDOXDgADNnzmTGjBmMGDHCMd9AxFUZBuzZAy+8AKVKQdu2sHSpGaJq14aPPybh1El6dffiZS8zRH3V6Ss6VtPdrCIiWUW6e6R2795NQEBA8vKNsUzBwcHMnj2bM2fOJIcqgPLly7N+/XqGDRvGZ599RsmSJfn444819YFkX0ePmpfu5s+HAwf+WV+sGPToAX36QK1aJCQl0Gt5Lxb/uhgPNw+WdF5C+yrtLStbRETSL91Byt/fP3mweGpmz55907pGjRrx448/pvdQIllHZCR89ZUZnnbu/Ge9jw+0b2+Gp2bNkh8abE+003N5T5b8tgRPN0+WdF5CuyrtrKldREQyTM/aE8moK1dg5UpYtAjCwiAx0Vxvs0HjxtCzJzzxBOTLl+Jj9kQ7PZb3YOlvS/F082RZl2W0qdwm8+sXEZG7piAlkh5Xr8K6dbB4Maxf/8+gcYA6dczw1K0blCyZ6sftiXa6L+vOsgPL8HL3YmnnpQpRIiJZmIKUyJ1cvQpr1sCSJeadd7Gx//yualXo3h26doVKlW67m/jEeLot7caKgyvwcvdieZfltKp0i0fAiIhIlqAgJZKaixfN8LRihRme/vXIIu67z3xYcPfuUKOGeSnvDuIT4+m6tCsrD67E292bFV1X0KJi2p9ZKSIirklBSuSG06fNMU8rVkB4+D9jnsDsberc2XzVrJmm8HRDfGI8XZZ0YdWhVXi7e7Oy20qa39fc8fWLiEimU5CSnMsw4JdfzAkyV62CH35I+fuaNaFDB3PA+P33pys83RCXEEeXpV1YfWg13u7erOq2iqD7ghz0BURExGoKUpKzxMXB9u3mgPHVq805n26w2eDhh83g1KGDeQnvbg6VEEenJZ1Y+/tafDx8WNVtFYH3Bt7lFxAREVeiICXZ35kzsGEDrF1rTlNw7do/v/PxMed3atsWWreG4sUdcsj/hqg13dfQtEJTh+xbRERch4KUZD92uzkp5saN5ut/jzNKVrw4tGplBqdmzSB3bocePjYhlo5fdWT94fXk8sjFmu5raFKhiUOPISIirkFBSrI+w4AjR8zeptBQ2LLFnLLgBpsN6tUzg1OrVuZz7tzS/ZjJNIlNiOWJxU+w4Y8N5PLIxdoea2lcvrFTjiUiItZTkJKsKTISIiLM8BQWlnKsE0DhwhAUBC1aQGAgFCni9JJiE2LpsLgDG//YiK+nL+t6rMO/nL/TjysiItZRkJKsISrKHCS+dav5+umnlL/39IQGDcxLdYGBULeu03qdUnPdfp32i9sTeiQUX09f1vdYT6NyjTLt+CIiYg0FKXFNly/Djh2wbZv5+vFHSEpKuc3995vPtAsMhMcfBz8/S0q9br9Ou0XtCPszjNyeuVnfcz2P3/O4JbWIiEjmUpAS13DqFHz99T+vn34yxz792733QpMmZngKCICiRa2p9V9i7DG0W9SOzX9uJrdnbjb03EDDexpaXZaIiGQSBSnJfAkJ8PPP5p11u3aZP48du3m7SpWgUSPw9zd/liqV2ZXeVow9hjYL27D16Fb8vPzY0HMDj5V9zOqyREQkEylIiXMZhtnb9P335uvbb80ZxGNiUm7n5ga1asFjj/3zKlHCkpLTIjo+mjYL2xB+LBw/Lz829tzIo2UftbosERHJZApS4ljnzlF0zx7c9u2DvXvN8HTmzM3b5csHjzwC9ev/88qTJ9PLzYjo+GhaL2xNxLEI8njlYWOvjTQo08DqskRExAIKUpIxhgHHj5tjmfbtMweD79mD56lT1P/vtu7u5sDwhx4yX/XrQ5UqmXpXnaNEx0fTakErth3fRh6vPGzqtYn6ZW76xiIikkMoSMmdXb1qPtx3/37z588/m+HpypWbNjVsNq6VKkXuhg1xe/BB89l1tWqBr2+ml+1o1+Kv0WpBK7Yf305e77xs6rWJR0o/YnVZIiJiIQUp+ceVK3DggPn67Tfz9euvZs9Tajw9oXp1MyjVqgV165JQrRpbd+ygZcuWuHl6Zmb1TnU17iotF7Tk6xNfk9c7L6G9Qnm49MNWlyUiIhZTkMpp4uLMO+QOH4bff4dDh8zX77+nPpbphpIlzctzNWqYP2vVgqpVwcsr5XZ2uzOrt8TVuKu0mN+Cb05+Qz7vfIT2DuWhUg9ZXZaIiLgABansxjDg/HkzLB09av7880/zWXRHjsCJEzfPz/RvJUtCtWpmSLrx8/77oWDBzPoGLiUqLooW81uw8+RO8vvkJ6x3GPVK1rO6LBERcREKUlmJYcDff8Pp0+brr7/g5Ml/XidOmD+vX7/9fnLnNie3rFz5n1elSuYrf/5M+SpZQVRcFM3nNWfXX7so4FOAsN5h1C1Z1+qyRETEhShIWS0uzgxHkZFw4cI/P8+du/l1+jTEx995nzYblC4N5cr987rvPjM83XefOSO4zebkL5a1XYm9QvP5zfn2r28p4FOAzX02U6dEHavLEhERF6MglRaGYc7GnZBgjgGKjTUDUGzsP6/oaPMVE2P+vHbNvNstKirl69KllK//TkyZFkWKmJfgSpaEMmXMV9myKX/+d+ySpNmV2CsEzQviu1PfUTBXQTb33kztErWtLktERFyQghTA2LF4fPwxLePj8XB3Nx+OaxjmT7sdEhOde3x3dyhUCAoX/udVrJj5Kl78n/elSpnLCklOczn2MkHzgvj+1PcUzFWQLX22UKt4LavLEhERF6UgBRAbi+3yZdJ1s763t/ny8TF/5s79z8vX1/yZN2/KV548UKBAylfBguYs31lwcsrs5nLsZQLnBvLD6R8olKsQW/ps4YHiD1hdloiIuDAFKYAXX8Teuzfbduygkb8/nt7eZrCx2cy5kjw8zJ833nt5KfhkM5euXyJwXiC7T++msG9htvTZQs1iNa0uS0REXJyCFJiDrwsUIPrIEXMwdjaaSFLu7NL1SzSb24w9Z/ZQ2LcwW/ts5f5i91tdloiIZAEKUpKjXbx+kaZzmrL37F6FKBERSTcFKcmx/o75m6Zzm7Lv7D6K+BZha/BWahStYXVZIiKShShISY4UGRNJ0zlN+encTxTNXZStfbZSvWh1q8sSEZEsRkFKcpzImEiazGnCz+d+pmjuooQHh1OtSDWryxIRkSxIQUpylAvRF2gypwn7z++nWO5ihAeHU7VIVavLEhGRLEpBSnKM89HnaTKnCb+c/4XifsUJDw6nSuEqVpclIiJZmIKU5Ajno8/TOKQxv174lRJ+JQgPDqdy4cpWlyUiIlmcgpRke+eunaPxnMb8duE3SuYpSXhwOJUKVbK6LBERyQYUpCRbO3vtLI1DGnMg8gCl8pQiPDicioUqWl2WiIhkEwpSkm2dvXaWgJAADkYeVIgSERGnUJCSbOnM1TM0ntOYg5EHKZ23NOHB4dxX8D6ryxIRkWxGQUqyndNXTxMQEsDvf/9OmbxlCA8O596C91pdloiIZEMKUpKtnIo6RUBIAIcvHqZsvrKEB4dToUAFq8sSEZFsys3qAkQc5d8h6p589xARHKEQJSIiTqUeKckW/or6i4CQAP64+IcZop6MoFz+claXJSIi2ZyClGR5J6+cJCAkgCOXjlAufzkigiO4J/89VpclIiI5gIKUZGknrpwgICSAPy/9Sfn85Yl4MoKy+cpaXZaIiOQQClKSZR2/fJyAkACOXj5KhQIVCA8OV4gSEZFMpSAlWdLxy8fxD/Hn2OVj3FvgXsKDwymTr4zVZYmISA6jICVZzrHLx/Cf7c/xK8e5t8C9RDwZQem8pa0uS0REciBNfyBZytFLR2k0uxHHrxynYsGKbHtym0KUiIhYRkFKsow/L/2Jf4g/J66coGLBioQHh1MqbymryxIRkRxMl/YkSzhy8QgBIQGcjDpJpUKVCA8Op2SeklaXJSIiOZyClLi8IxeP4B/iz19Rf1G5UGXCg8MpkaeE1WWJiIgoSIlr++PiH/jP9ufU1VNUKVyF8OBwivsVt7osERERQGOkxIUd/vtwcoiqWrgqEcERClEiIuJSFKTEJf3+9+/4h5ghqlqRaoQHh1PMr5jVZYmIiKSgS3vicg5FHiIgJIAz185QvUh1tgZvpWjuolaXJSIichMFKXEpByMPEhASwNlrZ6lRtAZb+2ylSO4iVpclIiKSKl3aE5dx4MKB5BB1f9H7FaJERMTlqUdKXMJvF36jcUhjzkWfo2axmmzps4XCvoWtLktEROS2FKTEcr+e/5XGcxpzPvo8DxR7gC19tlDIt5DVZYmIiNyRLu2JpX45/wsBIQGcjz5PreK1FKJERCRLUY+UWOaX87/QOKQxF2IuULt4bTb32UzBXAWtLktERCTN1CMllth/bj8BIQFciLlAnRJ1FKJERCRLUpCSTPfT2Z8ICAkgMiaSuiXqsrm3QpSIiGRNurQnmeqnsz/RZE4T/r7+N/VK1iOsdxj5ffJbXZaIiEiGqEdKMs2+s/toPKcxf1//m4dKPaQQJSIiWZ56pCRT7D2zlyZzmnAp9hIPl3qYTb02kc8nn9VliYiI3BX1SInT/Xjmx+QQ9UjpRxSiREQk21CQEqfac3oPTec05VLsJeqXrq8QJSIi2YqClDjN7tO7aTrXDFENyjRgY6+N5PXOa3VZIiIiDpOhIDVlyhTKly+Pj48PdevWZceOHbfcNiIiApvNdtPr4MGDGS5aXN/u07tpOqcpl2Mv82iZR9nYUyFKRESyn3QHqcWLFzN06FBeffVV9u7dS8OGDWnRogUnTpy47ecOHTrEmTNnkl8VK1bMcNHi2n6P/p3mC5tzJe4Kj5V9jA09N5DHO4/VZYmIiDhcuoPUhx9+SL9+/ejfvz9Vq1Zl0qRJlClThqlTp972c0WLFqV48eLJL3d39wwXLa7ru1PfMe7IOKLiomhYtqFClIiIZGvpmv4gPj6ePXv28Morr6RYHxgYyM6dO2/72dq1axMbG0u1atUYM2YMAQEBt9w2Li6OuLi45OWoqCgA7HY7drs9PSWn2Y39Omv/OcG3f31Lq0WtiEmK4bHSj7Gqyyq8bd5q0wzQ+egYakfHUDs6htrRcZzdlunZb7qCVGRkJImJiRQrVizF+mLFinH27NlUP1OiRAm++OIL6tatS1xcHHPnzqVJkyZERETw+OOPp/qZCRMmMH78+JvWh4aG4uvrm56S0y0sLMyp+8+uDkYfZPyR8VxPuk713NUZXGAw2zdvt7qsLE/no2OoHR1D7egYakfHcVZbxsTEpHlbm2EYRlo3Pn36NKVKlWLnzp3Ur18/ef1bb73F3Llz0zyAvE2bNthsNlavXp3q71PrkSpTpgyRkZHkzeucAct2u52wsDCaNWuGp6enU46RXe08uZPWi1tzLf4aj5d9nIH5BtKmeRu1413Q+egYakfHUDs6htrRcZzdllFRURQuXJgrV67cMXekq0eqcOHCuLu739T7dP78+Zt6qW7nkUceYd68ebf8vbe3N97e3jet9/T0dPrJlxnHyE6+PvE1rRa1ItoeTePyjVneaTkRYRFqRwdROzqG2tEx1I6OoXZ0HGe1ZXr2ma7B5l5eXtStW/emrrSwsDAaNGiQ5v3s3buXEiVKpOfQ4oJ2HN9B83nNibZH06R8E9Z0X4Ovp3MvvYqIiLiSdD9rb/jw4fTu3Zt69epRv359vvjiC06cOMGAAQMAGDVqFKdOnWLOnDkATJo0iXLlylG9enXi4+OZN28ey5YtY9myZY79JpKpth3bRqsFZk9UswrNWNVtFbk8c2kQpYiI5CjpDlJdu3bl77//5vXXX+fMmTPUqFGD9evXc8899wBw5syZFHNKxcfHM2LECE6dOkWuXLmoXr0669ato2XLlo77FpKpIo5F0GpBK2LsMQTeG8jKrivJ5ZnL6rJEREQyXbqDFMDAgQMZOHBgqr+bPXt2iuWRI0cycuTIjBxGXFD40XBaL2xNjD2GoHuDWNltJT4ePlaXJSIiYgk9a0/SbOvRrck9Uc3va64QJSIiOZ6ClKTJlj+30HpBa64nXKdlxZas6LpCIUpERHI8BSm5o81/bqb1QjNEtarYiuVdlitEiYiIoCAldxB6JJQ2C9sQmxBL60qtWdZlGd4eN8/xJSIikhMpSMktbfpjE20XtiU2IZa2lduytPNShSgREZF/UZCSVG38YyPtFrUjLjGOdpXbsaTzEoUoERGR/1CQkptsOLwhOUS1r9Kerzp/hZe7l9VliYiIuBwFKUlh/eH1tF/cnvjEeDpU6cBXnRSiREREbkVBSpKt/X0tHRZ3ID4xno5VO7K402I83fVgTRERkVvJ0Mzmkv2s/X0tTyx+AnuSnU7VOrHgiQUKUSIiInegHilh9aHVySGqc7XOClEiIiJppCCVw606uIpOX3XCnmSna/WuLOioECUiIpJWClI52IoDK+i0xAxR3Wp0Y94T8/Bw09VeERGRtFKQyqGWH1hOl6VdSEhKoHuN7sztMFchSkREJJ0UpHKgZb8to+vSriQkJdDz/p7M6TBHIUpERCQD9K9nDrPk1yV0X9adRCORXjV7MbvdbNzd3K0uS0REJEtSj1QO8tWvXyWHqN41eytEiYiI3CUFqRxi0S+L6LGsB4lGIsEPBDOr3SyFKBERkbukIJUDLNy/kJ7Le5JoJPJUraeY0XaGQpSIiIgDKEhlcwv2L6DXil4kGUn0q92PL9t+qRAlIiLiIApS2di8n+fRe0Vvkowk+tfuzxdtvsDNpj9yERERR9G/qtnUnJ/m0GdFH5KMJJ6u8zSft/lcIUpERMTB9C9rNhSyL4QnVz6JgcGzdZ9lWutpClEiIiJOoH9ds5lZe2fx1KqnMDB4rt5zTGk1RSFKRETESfQvbDYyc+9M+q3uh4HBwHoD+azlZwpRIiIiTqR/ZbOJL3/8MjlEDXpwEJ+2/BSbzWZ1WSIiItmaglQ2MH3PdJ5e8zQAzz/0PJ+0+EQhSkREJBMoSGVxX+z5gmfWPgPACw+/wOTmkxWiREREMomCVBb2+e7PeXbtswAMfXgoHwV9pBAlIiKSiRSksqhpu6cxYN0AAIY/MpwPgz5UiBIREclkClJZ0JQfpvDcuucAGFF/BBMDJypEiYiIWEBBKov59PtPGbR+EAAjG4zkvWbvKUSJiIhYREEqC/nku094fsPzALz86Mu80/QdhSgRERELKUhlEZO/ncyQjUMAGPXYKCY0maAQJSIiYjEFqSxg0reTGLppKACjHxvNW43fUogSERFxAQpSLu7DXR8ybNMwAMY0HMObjd9UiBIREXERClIu7IOdH/Bi6IsAvPb4a7we8LpClIiIiAtRkHJR73/zPiPCRgAwttFYxgeMV4gSERFxMQpSLujdr99l5OaRAIxrNI5x/uOsLUhERERS5WF1AZLSO1+/w6gtowAY7z+e1xq9ZnFFIiIicisKUi7kre1vMSZ8DABvBLzBmMfHWFyRiIiI3I6ClIt4c/ub/F/4/wHwVuO3GN1wtMUViYiIyJ1ojJQLeH3b68kh6u3GbytEiYiIZBHqkbLY+IjxjNs2DoB3mrzDy4+9bG1BIiIikmYKUhYxDIPx28Yzftt4AN5r+h4vPfqSxVWJiIhIeihIWcAwDMZGjOWN7W8A8H6z9xnRYITFVYmIiEh6KUhlMsMw+L/w/+OtHW8B8EHgBwyvP9ziqkRERCQjFKQykWEYjNk6hre/fhuADwM/ZFj9YRZXJSIiIhmlIJVJDMNg9JbRvPPNOwBMCprEC4+8YHFVIiIicjcUpDKBYRi8svkV3tv5HgCTm09myMNDLK5KRERE7paClJMZhsHIsJFM3DURgE9afMLghwZbXJWIiIg4goKUExmGwUthL/HBrg8A+LTFpwx6aJDFVYmIiIijKEg5iWEYvBj6Ih99+xEAn7X8jIEPDrS4KhEREXEkBSknMAyD4ZuGM+m7SQBMbTWVAfUGWFuUiIiIOJyClIMZhsHQjUP5+PuPAfi89ec8U/cZi6sSERERZ1CQciDDMHhh4wt88v0nAHzR+guervu0xVWJiIiIsyhIOYhhGDy/4Xk+++EzAKa3mU7/Ov0trkpEREScSUHKAZKMJAavH8zU3VOxYePLtl/St3Zfq8sSERERJ1OQuktJRhKD1g1i2p5p2LAxo+0Mnqr9lNVliYiISCZQkLoLSUYSA9cN5PM9n2PDxqx2swiuFWx1WSIiIpJJFKQyKMlIYsDaAUz/cbpClIiISA6lIJUBSUYSz655li/3fombzY2Q9iH0qtnL6rJEREQkkylIpVOSkcTTq59m5r6ZuNncmNN+Dj1r9rS6LBEREbGAglQ6JBlJ9F/dn1n7ZuFmc2Nuh7n0uL+H1WWJiIiIRRSk0igxKZH+a/oze99s3GxuzH9iPt1qdLO6LBEREbGQglQaJCYl0nd1X+b8NAd3mzvzn5hP1xpdrS5LRERELKYgdQeJSYk8teop5v48F3ebOws7LqRz9c5WlyUiIiIuQEHqNhKTEgleGcz8/fNxt7mzqNMiOlXrZHVZIiIi4iIUpG4hISmB4JXBLNi/AA83DxZ1XETHah2tLktERERciIJUKhKSEuizog8Lf1mIh5sHX3X6ig5VO1hdloiIiLgYt4x8aMqUKZQvXx4fHx/q1q3Ljh07brv9tm3bqFu3Lj4+PlSoUIFp06ZlqNjMkJCUQK/lvZJD1JLOSxSiREREJFXpDlKLFy9m6NChvPrqq+zdu5eGDRvSokULTpw4ker2R48epWXLljRs2JC9e/cyevRohgwZwrJly+66eEdLMBLovbI3i39djKebJ0s7L6V9lfZWlyUiIiIuKt1B6sMPP6Rfv37079+fqlWrMmnSJMqUKcPUqVNT3X7atGmULVuWSZMmUbVqVfr370/fvn2ZOHHiXRfvSPZEOx8e+5BlB5fh6ebJsi7LaFelndVliYiIiAtLV5CKj49nz549BAYGplgfGBjIzp07U/3Mrl27bto+KCiI3bt3Y7fb01muc9gT7fRa2YudV3bi5e7F8q7LaVO5jdVliYiIiItL12DzyMhIEhMTKVasWIr1xYoV4+zZs6l+5uzZs6lun5CQQGRkJCVKlLjpM3FxccTFxSUvR0VFAWC3250Svvqs6sOKQyvwsHmwsP1CgsoHuUzIy2putJva7+6oHR1D7egYakfHUDs6jrPbMj37zdBdezabLcWyYRg3rbvT9qmtv2HChAmMHz/+pvWhoaH4+vqmt9w7qnS9Er5uvrxY7kXcj7iz/sh6hx8jpwkLC7O6hGxB7egYakfHUDs6htrRcZzVljExMWneNl1BqnDhwri7u9/U+3T+/Pmbep1uKF68eKrbe3h4UKhQoVQ/M2rUKIYPH568HBUVRZkyZQgMDCRv3rzpKTlNWtKSZ68+yw87fqBZs2Z4eno6/Bg5hd1uJywsTO14l9SOjqF2dAy1o2OoHR3H2W1540pYWqQrSHl5eVG3bl3CwsLo0OGfKQHCwsJo1y71gdn169dnzZo1KdaFhoZSr169W355b29vvL29b1rv6enptJOvSJ4iTj9GTqJ2dAy1o2OoHR1D7egYakfHcVZbpmef6b5rb/jw4Xz55ZfMnDmTAwcOMGzYME6cOMGAAQMAszepT58+ydsPGDCA48ePM3z4cA4cOMDMmTOZMWMGI0aMSO+hRURERFxKusdIde3alb///pvXX3+dM2fOUKNGDdavX88999wDwJkzZ1LMKVW+fHnWr1/PsGHD+OyzzyhZsiQff/wxHTvqcSsiIiKStWVosPnAgQMZOHBgqr+bPXv2TesaNWrEjz/+mJFDiYiIiLisDD0iRkREREQUpEREREQyTEFKREREJIMUpEREREQySEFKREREJIMUpEREREQySEFKREREJIMUpEREREQySEFKREREJIMUpEREREQySEFKREREJIMUpEREREQySEFKREREJIMUpEREREQySEFKREREJIMUpEREREQySEFKREREJIM8rC4gLQzDACAqKsppx7Db7cTExBAVFYWnp6fTjpPdqR0dQ+3oGGpHx1A7Ooba0XGc3ZY38saN/HE7WSJIXb16FYAyZcpYXImIiIjkFFevXiVfvny33cZmpCVuWSwpKYnTp0+TJ08ebDabU44RFRVFmTJlOHnyJHnz5nXKMXICtaNjqB0dQ+3oGGpHx1A7Oo6z29IwDK5evUrJkiVxc7v9KKgs0SPl5uZG6dKlM+VYefPm1QnuAGpHx1A7Ooba0THUjo6hdnQcZ7blnXqibtBgcxEREZEMUpASERERySAFqf/x9vZm7NixeHt7W11KlqZ2dAy1o2OoHR1D7egYakfHcaW2zBKDzUVERERckXqkRERERDJIQUpEREQkgxSkRERERDJIQUpEREQkg3JMkJoyZQrly5fHx8eHunXrsmPHjttuv23bNurWrYuPjw8VKlRg2rRpmVSp60tPW0ZERGCz2W56HTx4MBMrdi3bt2+nTZs2lCxZEpvNxsqVK+/4GZ2PqUtvW+p8vNmECRN48MEHyZMnD0WLFqV9+/YcOnTojp/TOZlSRtpR52Pqpk6dSs2aNZMn26xfvz4bNmy47WesPB9zRJBavHgxQ4cO5dVXX2Xv3r00bNiQFi1acOLEiVS3P3r0KC1btqRhw4bs3buX0aNHM2TIEJYtW5bJlbue9LblDYcOHeLMmTPJr4oVK2ZSxa4nOjqaBx54gE8//TRN2+t8vLX0tuUNOh//sW3bNgYNGsS3335LWFgYCQkJBAYGEh0dfcvP6Jy8WUba8QadjymVLl2ad955h927d7N7924aN25Mu3bt+PXXX1Pd3vLz0cgBHnroIWPAgAEp1lWpUsV45ZVXUt1+5MiRRpUqVVKse/bZZ41HHnnEaTVmFelty/DwcAMwLl26lAnVZT2AsWLFittuo/MxbdLSljof7+z8+fMGYGzbtu2W2+icvLO0tKPOx7QrUKCA8eWXX6b6O6vPx2zfIxUfH8+ePXsIDAxMsT4wMJCdO3em+pldu3bdtH1QUBC7d+/Gbrc7rVZXl5G2vKF27dqUKFGCJk2aEB4e7swysx2dj46n8/HWrly5AkDBggVvuY3OyTtLSzveoPPx1hITE1m0aBHR0dHUr18/1W2sPh+zfZCKjIwkMTGRYsWKpVhfrFgxzp49m+pnzp49m+r2CQkJREZGOq1WV5eRtixRogRffPEFy5YtY/ny5VSuXJkmTZqwffv2zCg5W9D56Dg6H2/PMAyGDx/OY489Ro0aNW65nc7J20trO+p8vLX9+/fj5+eHt7c3AwYMYMWKFVSrVi3Vba0+Hz2cfgQXYbPZUiwbhnHTujttn9r6nCg9bVm5cmUqV66cvFy/fn1OnjzJxIkTefzxx51aZ3ai89ExdD7e3uDBg/n555/5+uuv77itzslbS2s76ny8tcqVK7Nv3z4uX77MsmXLCA4OZtu2bbcMU1aej9m+R6pw4cK4u7vf1GNy/vz5mxLsDcWLF091ew8PDwoVKuS0Wl1dRtoyNY888giHDx92dHnZls5H59L5aHr++edZvXo14eHhlC5d+rbb6py8tfS0Y2p0Ppq8vLy47777qFevHhMmTOCBBx5g8uTJqW5r9fmY7YOUl5cXdevWJSwsLMX6sLAwGjRokOpn6tevf9P2oaGh1KtXD09PT6fV6uoy0pap2bt3LyVKlHB0edmWzkfnyunno2EYDB48mOXLl7N161bKly9/x8/onLxZRtoxNTn9fLwVwzCIi4tL9XeWn4+ZMqTdYosWLTI8PT2NGTNmGL/99psxdOhQI3fu3MaxY8cMwzCMV155xejdu3fy9n/++afh6+trDBs2zPjtt9+MGTNmGJ6ensbSpUut+gouI71t+dFHHxkrVqwwfv/9d+OXX34xXnnlFQMwli1bZtVXsNzVq1eNvXv3Gnv37jUA48MPPzT27t1rHD9+3DAMnY/pkd621Pl4s+eee87Ily+fERERYZw5cyb5FRMTk7yNzsk7y0g76nxM3ahRo4zt27cbR48eNX7++Wdj9OjRhpubmxEaGmoYhuudjzkiSBmGYXz22WfGPffcY3h5eRl16tRJcUtqcHCw0ahRoxTbR0REGLVr1za8vLyMcuXKGVOnTs3kil1Xetry3XffNe69917Dx8fHKFCggPHYY48Z69ats6Bq13Hjluf/voKDgw3D0PmYHultS52PN0ut/QBj1qxZydvonLyzjLSjzsfU9e3bN/nfmCJFihhNmjRJDlGG4Xrno80w/jciS0RERETSJduPkRIRERFxFgUpERERkQxSkBIRERHJIAUpERERkQxSkBIRERHJIAUpERERkQxSkBIRERHJIAUpERERkQxSkBIRERHJIAUpERERkQxSkBIRERHJIAUpERERkQz6fyYk08K4+kmPAAAAAElFTkSuQmCC",
      "text/plain": [
       "Figure(PyObject <Figure size 700x700 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Start at right\n",
    "a = 0.0;\n",
    "b = 3.0;\n",
    "x = range(a, b, 100)\n",
    "x_k = b;\n",
    "figure(figsize=[7,7])\n",
    "title(L\"Starting to the right, at $x_0 =$\"*\"$b\")\n",
    "grid(true)\n",
    "plot(x, x, \"g\")\n",
    "plot(x, g_2.(x), \"r\")\n",
    "println(\"x_0 = $x_k\")\n",
    "for k in 1:iterations\n",
    "    g_x_k = g_2(x_k)\n",
    "    # Graph evalation of g(x_k) from x_k:\n",
    "    plot([x_k, x_k], [x_k, g_2(x_k)], \"b\")\n",
    "    x_k_plus_1 = g_2(x_k)\n",
    "    #Connect to the new x_k on the line y = x:\n",
    "    plot([x_k, g_2(x_k)], [x_k_plus_1, x_k_plus_1], \"b\")\n",
    "    # Update names: the old x_k+1 is the new x_k\n",
    "    x_k = x_k_plus_1\n",
    "    println(\"x_$(k) = $x_k\")\n",
    "end;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, things go awry if we try to compute the other fixed point, $p=4$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_0 = 4.001\n",
      "x_1 = 4.0016002\n",
      "x_2 = 4.002560832128009\n",
      "x_3 = 4.004098642977052\n",
      "x_4 = 4.006561188538134\n",
      "x_5 = 4.0105065115000205\n",
      "x_6 = 4.0168324957568124\n",
      "x_7 = 4.026988659793581\n",
      "x_8 = 4.043327533221221\n",
      "x_9 = 4.06969950818096\n",
      "x_10 = 4.112490817377671\n",
      "x_11 = 4.182516144603133\n",
      "x_12 = 4.29868825997317\n",
      "x_13 = 4.495744151286233\n",
      "x_14 = 4.842343094764873\n",
      "x_15 = 5.489657329483409\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 700x700 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Start near the other fixed point, p=4\n",
    "\n",
    "a = 3.5;\n",
    "b = 5.0;\n",
    "x = range(a, b, 100)\n",
    "x_k = 4.001\n",
    "iterations = 15\n",
    "\n",
    "figure(figsize=[7,7])\n",
    "title(L\"Starting at $x_0 =$\"*\"$x_k\")\n",
    "grid(true)\n",
    "plot(x, x, \"g\")\n",
    "plot(x, g_2.(x), \"r\")\n",
    "println(\"x_0 = $x_k\")\n",
    "for k in 1:iterations\n",
    "    g_x_k = g_2(x_k)\n",
    "    # Graph evalation of g(x_k) from x_k:\n",
    "    plot([x_k, x_k], [x_k, g_2(x_k)], \"b\")\n",
    "    x_k_plus_1 = g_2(x_k)\n",
    "    #Connect to the new x_k on the line y = x:\n",
    "    plot([x_k, g_2(x_k)], [x_k_plus_1, x_k_plus_1], \"b\")\n",
    "    # Update names: the old x_k+1 is the new x_k\n",
    "    x_k = x_k_plus_1\n",
    "    println(\"x_$(k) = $x_k\")\n",
    "end;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{exercise-start}\n",
    ":label: fixed-point-iteration-exercise-1\n",
    "```\n",
    "The equation\n",
    "$x^3 -2x + 1 = 0$\n",
    "can be written as a fixed point equation in many ways, including\n",
    "1. $\\displaystyle x = \\frac{x^3 + 1}{2}$\n",
    "<br>\n",
    "and\n",
    "2. $x = \\sqrt[3]{2x-1}$\n",
    "\n",
    "For each of these options:\n",
    "\n",
    "(a) Verify that its fixed points do in fact solve the above cubic equation.\n",
    "\n",
    "(b) Determine whether fixed point iteration with it will converge to the solution $r=1$.\n",
    "(assuming a \"good enough\" initial approximation).\n",
    "\n",
    "**Note:** computational experiments can be a useful start, but prove your answers mathematically!\n",
    "```{exercise-end}\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{exercise-start}\n",
    ":label: fixed-point-iteration-exercise-2\n",
    "```\n",
    "Consider the task of computing the positive $n$-th root $r = a^{1/n}$ of a positive number $a$ by fixed-point iteration $x_{k+1} = g(x_k)$.\n",
    "Two possible functions to use are\n",
    "\n",
    "$$\n",
    "g_1(x) = \\frac{x + a/x^{n-1}}{2} \\quad \\text{ and } \\quad\n",
    "g_2(x) = \\frac{(n-1)x + a/x^{n-1}}{n},\n",
    "$$ (fpi-exercise2-g-options)\n",
    "\n",
    "both generalizing the classic formula for computing square roots, $\\displaystyle g(x) = \\frac{x + a/x}{2}$.\n",
    "\n",
    "a) Verify that each does indeed have $a^{1/n}$ as a fixed point.\n",
    "\n",
    "b) Test each method for convergence (as usual, you may assume a sufficiently good initial approximation).\n",
    "\n",
    "c) Your results above should identify one method as \"superior\" in that it has super-linear convergence: which one?\n",
    "\n",
    "d) Show that this superior method converges for *any* positive initial approximation,\n",
    "even though this is not guaranteed by the general theorems on fixed point iteration.\n",
    "\n",
    "```{exercise-end}\n",
    "```"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Julia 1.11.4",
   "language": "julia",
   "name": "julia-1.11"
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  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.11.4"
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