{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Error Formulas for Polynomial Collocation\n",
    "\n",
    "**Last Revised on Wednesday February 17.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References:**\n",
    "- Section 3.2.1 *Interpolation error formula* of [Sauer](../references.html#Sauer)\n",
    "- Section 3.1 *Interpolation and the Lagrange Polynomial* of [Burden&Faires](../references.html#Burden-Faires)\n",
    "- Section 4.2 *Errors in Polynomial Interpolation* of [Chenney&Kincaid](../references.html#Chenney-Kincaid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "When a polynomial $P_n$ is given by collocation to $n+1$ points $(x_i, y_i)$, $y_i = f(x_i)$ on the graph of a function $f$, one can ask how accurate it is as an approximation of $f$ at points $x$ other than the nodes: what is the error $E(x) = f(x) - P(x)$?\n",
    "\n",
    "As is often the case, the result is motivated by considering the simplest \"non-trival case\":\n",
    "$f$ a polynomial of degree one too high for an exact fit, so of degree $n+1$.\n",
    "The result is also analogous to the familiar error formula for Taylor polynonial approximations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import linspace, polyfit, polyval, ones_like\n",
    "from  matplotlib.pyplot import figure, plot, title, grid, legend"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Error in $P_n(x)$ collocating a polynomial of degree $n+1$\n",
    "\n",
    "With $f(x) = c_{n+1} x^{n+1} + c_{n} x^{n} + \\cdots + c_0$ a polynomial of degree $n+1$ and $P_n(x)$ the unique polynomial of degree at most $n$ that collocates with it at the $n+1$ nodes $x_0, \\dots x_n$, the error\n",
    "\n",
    "$$ E_n(x) = f(x) - P(x) $$\n",
    "\n",
    "is a polynomial of degree $n+1$ with all its roots known: the nodes $x_i$.\n",
    "Thus it can be factorized as\n",
    "\n",
    "$$\\begin{split}\n",
    "E_n(x) &= C (x-x_0) \\cdot (x-x_1) \\cdots (x-x_n)\\\\\n",
    "       &= Cx^{n+1} + \\text{lower powers of $x$.}\n",
    "\\end{split}$$\n",
    "\n",
    "On the other hand, the only term of degree $x^{n+1}$ in $f(x) - P(x)$ is the leading term of $f(x)$, $c_{n+1} x^{n+1}$.\n",
    "Thus $C = c_{n+1}$.\n",
    "\n",
    "It will be convenient to note that the order $n+1$ derivative of $f$ is the constant\n",
    "$f^{(n+1)}D^{n+1}f(x) = (n+1)! c_{n+1}$, so the error can be written as\n",
    "\n",
    "$$\n",
    "E_n(x) = f(x) - P_n(x) = \\frac{D^{n+1}f(x)}{(n+1)!} (x-x_0) \\cdots (x-x_n)\n",
    "= \\frac{D^{n+1}f(x)}{(n+1)!}\\prod\\limits_{i=0}^n (x - x_i).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Error in $P_n(x)$ collocating a sufficiently differentiable function\n",
    "\n",
    "**Theorem 1.**\n",
    "For a function $f$ with continuous derivative of order $n+1$ $D^{n+1}f$,\n",
    "the polynomial $P_n$ of degree at most $n$ that fits the points $(x_i, f(x_i))$ $0 \\leq i \\leq n$ differs from $f$ by\n",
    "\n",
    "$$\n",
    "E_n(x) = f(x) - P_n(x) = \\frac{D^{n+1}f(\\xi_x)}{(n+1)!}\\prod\\limits_{i=0}^n (x - x_i)\n",
    "$$\n",
    "\n",
    "for some value of $\\xi_x$ that is amongst the $n+2$ points $x_0, \\dots x_n$ and $x$.\n",
    "\n",
    "In particular, when $a \\leq x_0 < x_1 \\cdots < x_n \\leq b$ and $x \\in [a,b]$, then also $\\xi_x \\in [a, b]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note the similarity to the error formula for the Taylor polynomial $p_n$ with center $x_0$:\n",
    "\n",
    "$$\n",
    "e_n(x) = f(x) - p_n(x) = \\frac{D^{n+1}f(\\xi)}{(n+1)!} (x-x_0)^{n+1},\\, \\text{some $\\xi$ between $x_0$ and $x$.}\n",
    "$$\n",
    "\n",
    "This is effectively the limit when all the $x_i_x$ congeal to $x_0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Error bound with equally spaced nodes is $O(h^{n+1})$, but ...\n",
    "\n",
    "An important special case is when there is a single parameter $h$ describing the spacing of the nodes; when they are the equally spaced values $x_i = a + i h$, $0 \\leq i \\leq n$, so that $x_0 = a$ and $x_n = b$ with $h = \\displaystyle \\frac{b-a}{n}$.\n",
    "Then there is a somewhat more practically usable error bound:\n",
    "\n",
    "**Theorem 2.**\n",
    "For $x \\in [a,b]$ and the above equaly spaced nodes in that interval $[a,b]$,\n",
    "\n",
    "$$\n",
    "| E_n(x) | = \\left| f(x) - P_n(x)\\right| \\leq \\frac{M_{n+1}}{n+1} h^{n+1}, = O(h^{n+1}),\n",
    "$$\n",
    "\n",
    "where $M_{n+1} = \\max\\limits_{x \\in [a,b]} | D^{n+1}f(x)|$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Possible failure of convergence\n",
    "\n",
    "A major practical problem with this error bound is that is does not in general guarantee convergence\n",
    "$P_n(x) \\to f(x)$ as $n \\to \\infty$ with fixed interval $[a, b]$, because in some cases $M_{n+1}$ grows too fast.\n",
    "\n",
    "A famous example is the \"Witch of Agnesi\" (so-called because it was introduced by Maria Agnesi,\n",
    "author of the first textbook on differential and integral calculus)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def agnesi(x):\n",
    "    \"\"\"An example sometime know as \"the Witch of Agnesi\",\n",
    "    after \n",
    "    \"\"\"\n",
    "    return 1/(1+x**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def graph_agnesi_collocation(a, b, n):\n",
    "    figure(figsize=[12, 6])\n",
    "    title(f\"The Witch of Agnesi and collocating polynomial of degree {n=}\")\n",
    "    x = linspace(a, b, 200)  # Plot 200 points instead of the default 50, as some fine detail is needed\n",
    "    agnesi_x = agnesi(x)\n",
    "    plot(x, agnesi_x, label=\"Witch of Agnesi\")\n",
    "    x_nodes = linspace(a, b, n+1)\n",
    "    y_nodes = agnesi(x_nodes)\n",
    "    c = polyfit(x_nodes, y_nodes, n)\n",
    "    P_n = polyval(c, x)\n",
    "    plot(x_nodes, y_nodes, 'r*', label=\"Collocation nodes\")\n",
    "    plot(x, P_n, label=\"P_n(x)\")\n",
    "    legend()\n",
    "    grid(True)\n",
    "\n",
    "    figure(figsize=[12, 6])\n",
    "    title(f\"Error curve\")\n",
    "    E_n = P_n - agnesi_x\n",
    "    plot(x, E_n)\n",
    "    grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Start with $n=4$, which seems somewhat well-behaved:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph_agnesi_collocation(a=-4, b=4, n=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now increase the number of inervals, doubling each time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph_agnesi_collocation(a=-4, b=4, n=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The curve fits better in the central part, but gets worse towards the ends!\n",
    "\n",
    "One hint as to why is to plot the polynomial factor in the error formula above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def graph_error_formula_polynomial(a, b, n):\n",
    "    figure(figsize=[12, 6])\n",
    "    title(f\"The polynomial factor in the error formula for degree {n=}\")\n",
    "    x = linspace(a, b, 200)  # Plot 200 points instead of the default 50, as some fine detail is needed\n",
    "    x_nodes = linspace(a, b, n+1)\n",
    "    polynomial_factor = ones_like(x)\n",
    "    for x_node in x_nodes:\n",
    "        polynomial_factor *= (x - x_node)\n",
    "    plot(x, polynomial_factor)\n",
    "    grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph_error_formula_polynomial(a=-4, b=4, n=4)\n",
    "graph_error_formula_polynomial(a=-4, b=4, n=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As n increases, it just gets worse:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
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     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph_agnesi_collocation(a=-4, b=4, n=16)\n",
    "graph_error_formula_polynomial(a=-4, b=4, n=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A Solution: piecewise (linear) interpolation\n",
    "\n",
    "A solution to this problem is to use collocation with just a fixed number of nodes $m$ as $h \\to 0$ and the total node count $n \\to \\infty$.\n",
    "That is, for each $x$, approximate $f(x)$ using just data from a suitable choice of $m+1$ nodes near $x$.\n",
    "Then $M_{m+1}$ is a constant, and one has the convergence result\n",
    "\n",
    "$$\n",
    "| E_n(x) \\leq \\frac{M_{m+1}}{m+1} h^{m+1}, = O(h^{m+1}), = O(1/n^{m+1})\n",
    "$$\n",
    "\n",
    "so long as $f$ has a continuous derivatives up to order $m+1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But then how does one get an approximation over a fixed interval of interest, $[a, b]$?\n",
    "\n",
    "One solution is to use multiple polynomials, by dividing the interval into numerous small ones.\n",
    "The simplest version of this is to divide it into $n$ sub-intervals of equal width $h=(b-a)/n$, separated at nodes\n",
    "$x_i = a + i h$, $0 \\leq i \\leq n$, and approximate $f(x)$ *linearly* on each sub-inerval by using the two surrounding nodes $x_i$ and $x_{i+1}$ determined by having $x_i \\leq x \\leq x_{i+1}$:\n",
    "this is **piecewise linear interpolation.**\n",
    "\n",
    "This gives the approximating function $L_n(x)$,\n",
    "and the above error formula, now with $m=1$ says that the worst absolute error anywhere in the interval $[a, b]$ is\n",
    "\n",
    "$$\n",
    "|E(x)| = |f(x) - L_n(x)| \\leq \\frac{M_2}{2} h^2 = \\frac{M_2 (b-a)^2}{2 n^2}, = O(1/n^2),\n",
    "$$\n",
    "\n",
    "with $M_2 = \\max\\limits_{x \\in [a,b]} | D^2f(x)|$.\n",
    "\n",
    "Now clearly, as $n \\to \\infty$, the error at each $x$-value converges to zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Preview: definite integrals (en route to solving differential equations)\n",
    "\n",
    "Integrating this piecewise linear approximation over interval $[a, b]$ gives the Compound Trapezoid Rule approximation of $\\int_a^b f(x) dx$.\n",
    "As we will soon see, this also has error at worst $O(h^2), = O(1/n^2)$:\n",
    "each doubling of effort reduces errors by a factor of about four.\n",
    "\n",
    "Also, you might have heard of Simpson's Rule for approximating definite integrals (and anyway, you will soon!):\n",
    "that uses piecewise quadratic interpolation and we will see that this improves the errors to $O(h^4), = O(1/n^4)$:\n",
    "each doubling of effort reduces errors by a factor of about 16."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Aside: computer graphics and smoother approximating curves\n",
    "\n",
    "Computer graphics often draws graphs from data points this way, most often with either piecewise linear or piecewise cubic ($m=3$) approximation.\n",
    "\n",
    "However, this always gives sharp \"corners\" at the nodes.\n",
    "That is unavoidable with piecewise linear curves, but for higher degrees there are modifications of this strategy that give smoother curves: piecewise cubics turn out to work very nicely for that."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "This work is licensed under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/)"
   ]
  }
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