p09.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# p09: Polynomial interpolation in equispaced and chebyshev points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format='svg'\n",
    "from numpy import pi,inf,linspace,arange,cos,polyval,polyfit\n",
    "from numpy.linalg import norm\n",
    "from matplotlib.pyplot import figure,subplot,plot,axis,title,text"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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       "<Figure size 1000x500 with 2 Axes>"
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   "source": [
    "N = 16\n",
    "xx = linspace(-1.01,1.01,400,True)\n",
    "figure(figsize=(10,5))\n",
    "for i in range(2):\n",
    "    if i==0:\n",
    "        s = 'equispaced points'; x = -1.0 + 2.0*arange(0,N+1)/N\n",
    "    if i==1:\n",
    "        s = 'Chebyshev points'; x = cos(pi*arange(0,N+1)/N)\n",
    "    subplot(1,2,i+1)\n",
    "    u = 1.0/(1.0 + 16.0*x**2)\n",
    "    uu = 1.0/(1.0 + 16.0*xx**2)\n",
    "    p = polyfit(x,u,N)\n",
    "    pp= polyval(p,xx)\n",
    "    plot(x,u,'o',xx,pp)\n",
    "    axis([-1.1, 1.1, -1.0, 1.5])\n",
    "    title(s)\n",
    "    error = norm(uu-pp, inf)\n",
    "    text(-0.6,-0.5,'max error='+str(error));"
   ]
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