{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial Collocation (Interpolation/Extrapolation) and Approximation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Last revised on August 27, 2025**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- {cite}`Chasnov` Section 5.1, *Polynomial interpolation**.\n",
    "\n",
    "- {cite}`Sauer` Section 3.1, *Data and Interpolating Functions*.\n",
    "\n",
    "- {cite}`Burden-Faires` Section 3.1, *Interpolation and the Lagrange Polynomial*.\n",
    "\n",
    "- {cite}`Dionne` Chapter 6, *Polynomial Interpolation*.\n",
    "\n",
    "- {cite}`Chenney-Kincaid` Section 4.1, *Polynomial Interpolation*.\n",
    "\n",
    "%- {cite}`Kincaid-Chenney` ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "Numerical methods for dealing with functions require describing them, at least approximately, using a finite list of numbers, and the most basic approach is to approximate by a polynomial.\n",
    "(Other important choices are rational functions and \"trigonometric polynomials\": sums of multiples of sines and cosines.)\n",
    "Such polynomials can then be used to aproximate derivatives and integrals.\n",
    "\n",
    "The simplest idea for approximating $f(x)$ on domain $[a, b]$ is to start with a finite collection of **node** values $x_i \\in [a, b]$, $0 \\leq i \\leq n$ and then seek a polynomial $p$ which **collocates** with $f$ at those values: $p(x_i) = f(x_i)$ for $0 \\leq i \\leq n$.\n",
    "Actually, we can put the function aside for now, and simply seek a polynomial that passes through a list of points $(x_i, y_i)$; later we will achieve collocation with $f$ by choosing $y_i = f(x_i)$.\n",
    "\n",
    "In fact there are infinitely many such polynomials: given one, add to it any polynomial with zeros at all of the $n+1$ notes.\n",
    "So to make the problem well-posed, we seek the collocating polynomial of *lowest degree*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:theorem} Existence and uniqueness of a collocating polynomial\n",
    ":label: theorem-collocation\n",
    "\n",
    "Given $n+1$ distinct values $x_i$, $0 \\leq i \\leq n$, and corresponding $y$-values $y_i$,\n",
    "there is a unique polynomial $P$ of degree at most $n$ with $P(x_i) = y_i$ for $0 \\leq i \\leq n$.\n",
    "\n",
    "(*Note:* although the degree is typically $n$, it can be less; as an extreme example, if all $y_i$ are equal to $c$, then $P(x)$ is that constant $c$.)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Historically there are several methods for finding $P_n$ and proving its uniqueness, in particular, the *divided difference* method introduced by Newton and the *Lagrange polynomial* method.\n",
    "However for our purposes, and for most modern needs, a different method is easiest, and it also introduces a strategy that will be of repeated use later in this course: the **Method of Undertermined Coefficients** or **MUC**.\n",
    "\n",
    "In general, this method starts by assuming that the function wanted is a sum of unknown multiples of a collection of known functions.\n",
    "Here, $P(x) =  c_0 + c_1 x + \\cdots + c_{n-1} x^{n-1} + c_n x^n = \\sum_{j=0}^n c_j x^j$.\n",
    "<br>\n",
    "(*Note:* any of the $c_i$ could be zero, including $c_n$, in which case the degree is less than $n$.)\n",
    "<br>\n",
    "The unknown factors ($c_0 \\cdots c_n$) are the *undetermined coefficients.*\n",
    "\n",
    "Next one states the problem as a system of equations for these undetermined coefficients, and solves them.\n",
    "<br>\n",
    "Here, we have $n+1$ conditions to be met:\n",
    "\n",
    "$$P(x_i) = \\sum_{j=0}^n c_j x_i^j = y_i, \\quad 0 \\leq i \\leq n$$\n",
    "\n",
    "This is a system if $n+1$ simultaneous linear equations in $n+1$ unknowns, so the question of existence and uniqueness is exactly the question of whether the corresponding matrix is singular,\n",
    "and so is equivalent to the case of all $y_i = 0$ having *only* the solution with all\n",
    "$c_i = 0$.\n",
    "\n",
    "Back in terms of polynomials, this is the claim that the only polynomial of degree at most $n$ with zeros $x_0 \\dots x_n$.\n",
    "And this is true, because any non-trivial polynomial with those $n+1$ distinct roots is of degree at least $n+1$, so the only \"degree n\" polynomial fitting this data is $P(x) \\equiv 0$.\n",
    "The theorem is proven."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The proof of this theorem is completely constructive, and it gives the only numerical method we need.\n",
    "\n",
    "Briefly, the algorithm is this (indexing from 0 !)\n",
    "- Create the $n+1 \\times n+1$ matrix $V$ with elements\n",
    "\n",
    "$$v_{i,j} = x_i^j,\\; 0 \\leq i \\leq n, \\, 0 \\leq j \\leq n$$\n",
    "\n",
    "and the $n+1$-element column vector $y$ with elements $y_i$ as above.\n",
    "- Solve $V c = y$ for the vector of coefficients $c_j$ as above.\n",
    "\n",
    "I use the name $V$ because this is called the **Vandermonde Matrix.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Enable graph plotting; PyPlot is an interface to the Python package `matplotlib.pyplot`\n",
    "\n",
    "If this does not work in a downloaded notebook, see the instructions in the introduction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyPlot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# A helper function, short-hand for rounding\n",
    "import Base: round\n",
    "round(x, n) = Base.round(x, sigdigits=n);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example} Exact fit\n",
    ":label: interpolation-example-1\n",
    "\n",
    "As usual, I concoct a first example with known correct answer, by using a polynomial as $f$:\n",
    "\n",
    "$$ f(x) = 4 + 7x -2x^2 - 5x^3 + 2x^4 $$\n",
    "\n",
    "using the nodes $x_0 = 1$, $x_1 = 2$, $x_2= 0$, $x_3 = 3.3$ and $x_4 = 4$  (They do not need to be in order.)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "f(x) = 4 + 7x -2x^2 - 5x^3 + 2x^4;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:remark} A Julia shorthand for products\n",
    ":label: multiplication-by-juxtaposition-in-julia\n",
    "Note the convenient short-hand of writing products by juxtapositon, without `*`.\n",
    "This works when the first factor is a literal number, not a variable name.\n",
    "\n",
    "To avoid ambiguity with the use of dots for *vectorization* introduced below,\n",
    "avoid ending a floating point number with a period when it it an integer;\n",
    "for example you can use\n",
    "\n",
    "    f(x) = 4 + 7x ...\n",
    "or\n",
    "\n",
    "    f(x) = 4 + 7.0x ...\n",
    "\n",
    "but not\n",
    "\n",
    "    f(x) = 4 + 7.x + ...\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The x nodes 'x_i' are [1.0, 2.0, 0.0, 3.3, 4.0]\n",
      "The y values at the nodes are [6.0, 2.0, 4.0, 62.8192, 192.0]\n"
     ]
    }
   ],
   "source": [
    "xnodes = [1., 2., 0., 3.3, 4.]  # They do not need to be in order\n",
    "println(\"The x nodes 'x_i' are $(xnodes)\")\n",
    "ynodes = f.(xnodes)\n",
    "println(\"The y values at the nodes are $(round.(ynodes, 6))\")  # Rounded for nicer display"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:remark} Vectorizing a Julia function\n",
    ":label: julia-vectorization\n",
    "\n",
    "Appending the \"point\" to the function name (so it is `f.(...)` instead of `f(...)`) does **vectorization**:\n",
    "the function `f` is applied \"pointwise\", to each element of the input array `x_nodes` in turn,\n",
    "with the results returned in an aray of the same size and shape.\n",
    "\n",
    "\n",
    "If there are several arguments, all are vectorized.\n",
    "\n",
    "See {ref}`vectorization-of-functions` in the {doc}`julia-language-notes`.\n",
    "\n",
    "We will see this again soon.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Vandermonde matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "nnodes = length(xnodes)\n",
    "n = nnodes-1\n",
    "V = zeros(nnodes, nnodes)\n",
    "for i in 0:n\n",
    "    for j in 0:n\n",
    "        V[i+1,j+1] = xnodes[i+1]^j  # Shift the array indices up by one, since Julia counts from 1, not 0.\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solve, using our functions seen in earlier sections and gathered in {doc}`NumericalMethods`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "include(\"NumericalMethods.jl\")\n",
    "using .NumericalMethods: solvelinearsystem, printmatrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The coefficients of P are [4.0, 7.0, -2.0, -5.0, 2.0]\n"
     ]
    }
   ],
   "source": [
    "c_A = solvelinearsystem(V, ynodes)\n",
    "# It helps the visual presentation to round off;\n",
    "c_A = round.(c_A, 6)\n",
    "println(\"The coefficients of P are $c_A\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are correct!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compare the computed values P[i] to what they shoudl be (y_nodes[i])\n",
    "we use the convenient tool `zip` for looping over two or more \"parallel\" lists of values:\n",
    "`zip(x,y)` effectively produces a list of pairs `[(x[1], y[1]), (x[2], y[2]) ...)` up till one or both arrays runs out of elements,\n",
    "and it also works for three or more lists."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also check the resulting values of the polynomial:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "P = c_A[1] .+ c_A[2]*xnodes + c_A[3]*xnodes.^2 + c_A[4]*xnodes.^3 + c_A[5]*xnodes.^4;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:remark} Vectorizing operators and broadcasting values in Julia\n",
    ":label: vectorization-broadcasting-in-julia\n",
    "\n",
    "The period prefix in the exponential notation `.^` and the sum notation `.+` is **vectorization** and **broadcasting**:\n",
    "\n",
    "- **vectorization**: `a.^b` means that if one of `a` and `b` are arrays (or both are arrays, of the same shape and size) then the exponentiation is applied to each element in turn, producing an array of the same size and shape;\n",
    "\n",
    "- **brodcasting** of the addition: that first addition is \"number plus array\";\n",
    "the notation `.+` indicates that this be done by promoting the number to an array matching the other addend.\n",
    "\n",
    "Vectorization can also be applied to other binary operations such as multiplication and division.\n",
    "\n",
    "See the notes on\n",
    "{ref}`vectorization-and-broadcasting`\n",
    "in {doc}`julia-language-notes`.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can check the $y$ values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:remark} Zipping arrays together in Julia\n",
    ":label: zip-in-julia\n",
    "\n",
    "The function `zip` takes two or more arrays (preferably of the same size and shape) and turns them into an array with each element a tuple of values, one from the corresponding position in each input array.\n",
    "\n",
    "For example, with 1D arrays `x` and `y` of length n, `zip(x, y)` is `[ ( x[1], y[1] ), ( x[2], y[2] )  ... ( x[n], y[n] ) ]`\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(1.0) should be 6.0; it is 6.0\n",
      "P(2.0) should be 2.0; it is 2.0\n",
      "P(0.0) should be 4.0; it is 4.0\n",
      "P(3.3) should be 62.8192; it is 62.8192\n",
      "P(4.0) should be 192.0; it is 192.0\n"
     ]
    }
   ],
   "source": [
    "for (x, y, P_i) in zip(xnodes, ynodes, P)\n",
    "    println(\"P($x) should be $(round(y, 6)); it is $(round(P_i, 6))\")\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(polyfit-polyval)=\n",
    "## Functions for computing the coefficients and evaluating the polynomials\n",
    "\n",
    "We will use this procedure several times, so it time to put it into a functions.\n",
    "The names `polyfit` and `polyval` come from very similar functions that are standard in Python and Matlab.\n",
    "\n",
    "We also add a pretty printer for polynomials, and import the pretty printer `printmatrix` for matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "function polyfit(x, y)\n",
    "    # Compute the coeffients c_i of the polynomial of lowest degree that collocates the points (x[i], y[i]).\n",
    "    # These are returned in an array c of the same length as x and y, even if the degree is less than the normal length(x)-1,\n",
    "    # in which case the array has some trailing zeroes.\n",
    "    # The polynomial is thus p(x) = c[1] + c[2]x + ... c[n+1] x^n where n=length(x)-1, the nominal degree.\n",
    "\n",
    "    nnodes = length(x)\n",
    "    n = nnodes - 1\n",
    "    V = zeros(nnodes, nnodes)\n",
    "    for i in 0:n\n",
    "        for j in 0:n\n",
    "             V[i+1,j+1] = x[i+1]^j  # Shift the array indices up by one, since Julia counts from 1, not 0.\n",
    "        end\n",
    "    end\n",
    "    c = solvelinearsystem(V, y)\n",
    "    return c\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "function polyval(x; coeffs)  # coeffs has to be a keyword argument in order that only x gets vectorized\n",
    "    # Evaluate the polynomial with coefficients in c (as given by polyfit, for example).\n",
    "    n = length(coeffs) - 1\n",
    "    powers = collect(0:n)  # function collect turns the \"AbstractRange\" 0:n into an array of numbers.\n",
    "    y = sum(coeffs .* x.^powers)\n",
    "    return y\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "function displaypolynomial(c; sigdigits=6)\n",
    "    # Note that the function \"print\" does not end by going to a new line as `println` does;\n",
    "    # this is useful when you want to create a line of output piece-by-piece, as done here.\n",
    "\n",
    "    c = round.(c, sigdigits) # Clean up by rounding to sigdigits significant digits; yes, that's vectorization again.\n",
    "    degree=length(c)-1\n",
    "    print(\"P_$(degree)(x) = \")\n",
    "    print(c[1])\n",
    "    if degree > 0\n",
    "        c_1 = c[2]\n",
    "        if c_1 > 0\n",
    "            print(\" + $(c_1)x\")\n",
    "        elseif coeff < 0\n",
    "            print(\" - $(-c_1) x\")\n",
    "        end\n",
    "    end\n",
    "    if degree > 1\n",
    "        for j in 2:degree\n",
    "            c_j = c[j+1]\n",
    "            if c_j > 0\n",
    "                print(\" + $(c_j)x^$j\")\n",
    "            elseif c_j < 0\n",
    "                print(\" - $(-c_j)x^$j\")\n",
    "            end\n",
    "            # Note: if c_j=0, there is nothing to say.\n",
    "         end\n",
    "    end\n",
    "    println()\n",
    "end;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example} $f(x)$ not a polynomial of degree $\\leq n$\n",
    ":label: interpolation-example-2\n",
    "\n",
    "Make an exact fit impossible by using the same function but using only four nodes and reducing the degree of the interpolating $P$ to three:\n",
    "$x_0 = 1$, $x_1 = 2$, $x_2 = 3$ and $x_3 = 4$\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The x nodes 'x_i' are [1.0, 2.0, 3.0, 4.0]\n",
      "The y values at the nodes are [6.0, 2.0, 34.0, 192.0]\n",
      "P_3(x) = -44.0 + 107.0x - 72.0x^2 + 15.0x^3\n"
     ]
    }
   ],
   "source": [
    "xnodes = [1., 2., 3., 4.];\n",
    "println(\"The x nodes 'x_i' are $xnodes\")\n",
    "ynodes = f.(xnodes)\n",
    "println(\"The y values at the nodes are $ynodes\")\n",
    "c_B = polyfit(xnodes, ynodes);\n",
    "displaypolynomial(c_B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are several ways to assess the accuracy of this fit; we start graphically, and later consider the maximum and root-mean-square (RMS) errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "xplot = range(0.9, 4.1, 100)  # for graphing: go a bit beyond the nodes\n",
    "fplot = f.(xplot);\n",
    "Pplot = polyval.(xplot, coeffs=c_B);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1200x600 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[12,6])\n",
    "plot(xplot, fplot, label=\"f(x)\")\n",
    "plot(xnodes, ynodes, \"*\", label=\"nodes\")\n",
    "plot(xplot, Pplot, label=L\"y = $P_3(x)$\")\n",
    "legend()\n",
    "grid(true);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1200x600 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Perror = fplot - Pplot\n",
    "figure(figsize=[12,6])\n",
    "title(L\"Error in $P_3(x)$\")\n",
    "plot(xplot, Perror)\n",
    "plot(xnodes, zero(xnodes), \"*\")\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example} $f(x)$ not a polynomial at all\n",
    ":label: interpolation-example-3\n",
    "\n",
    "$f(x) = e^x$ with five nodes, equally spaced from $-1$ to $1$\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "g(x) = exp(x)\n",
    "a_g = -1.0\n",
    "b_g = 1.0;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "node x values -1.0:0.5:1.0\n",
      "node y values [0.3679, 0.6065, 1.0, 1.649, 2.718]\n",
      "P_4(x) = 1.0 + 0.9979x + 0.4996x^2 + 0.1773x^3 + 0.04344x^4\n"
     ]
    }
   ],
   "source": [
    "degree = 4\n",
    "n_nodes = degree + 1\n",
    "\n",
    "xnodes = range(a_g, b_g, n_nodes)\n",
    "gnodes = g.(xnodes)\n",
    "c_C = polyfit(xnodes, gnodes)\n",
    "println(\"node x values $xnodes\")\n",
    "println(\"node y values $(round.(gnodes, 4))\")\n",
    "displaypolynomial(c_C, sigdigits=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For comparison, the degree 4 Taylor polynomial for $e^x$ with center 0 is (to the same 6 significant digits)\n",
    "\n",
    "$$ 1 + x + 0.5 x^2 + 0.1667 x^3 + 0.04167 x^4$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "xplot = range(a_g - 0.2, b_g + 0.2, 100)  # Go a bit beyond the nodes in each direction\n",
    "gplot = g.(xplot)\n",
    "Pplot_g = polyval.(xplot, coeffs=c_C);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1200x600 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[12,6])\n",
    "plot(xplot, gplot, label=L\"y = g(x) = e^x\")\n",
    "plot(xnodes, gnodes, \"*\", label=\"nodes\")\n",
    "plot(xplot, Pplot_g, label=\"y = P(x)\")\n",
    "legend()\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1200x600 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Perror_g = gplot - Pplot_g\n",
    "figure(figsize=[12,6])\n",
    "degree = 8\n",
    "title(L\"Error in $P_4(x)$ for $g(x) = e^x$\")\n",
    "plot(xplot, Perror_g)\n",
    "plot(xnodes, zero(xnodes), \"*\")\n",
    "grid(true)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.11.4",
   "language": "julia",
   "name": "julia-1.11"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
