{"metadata": {"name": "", "signature": "sha256:814f991faaa5055ad8fe589e1e7b005616e0912b60a73061319ffd4c4a515d3d"}, "nbformat_minor": 0, "worksheets": [{"metadata": {}, "cells": [{"cell_type": "markdown", "metadata": {}, "source": ["# Monomial interpolation"]}, {"cell_type": "code", "outputs": [], "collapsed": false, "input": ["import numpy as np\n", "import numpy.linalg as la\n", "import matplotlib.pyplot as pt"], "prompt_number": 2, "language": "python", "metadata": {}}, {"cell_type": "code", "outputs": [], "collapsed": false, "input": ["x = np.linspace(0, 1, 200)"], "prompt_number": 3, "language": "python", "metadata": {}}, {"cell_type": "markdown", "metadata": {}, "source": ["Now plot the monomial basis on the interval [0,1] up to $x^9$."]}, {"cell_type": "code", "outputs": [{"output_type": "pyout", "metadata": {}, "prompt_number": 4, "text": [""]}, {"output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEACAYAAABI5zaHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "metadata": {}, "text": [""]}], "collapsed": false, "input": ["n = 10\n", "\n", "for i in range(n):\n", " pt.plot(x, x**i)\n", " \n", "pt.vlines(np.linspace(0, 1, n), 0, 1, alpha=0.5, linestyle=\"--\")"], "prompt_number": 4, "language": "python", "metadata": {}}, {"cell_type": "markdown", "metadata": {}, "source": ["* How do the entries of the Vandermonde matrix relate to this plot?"]}, {"cell_type": "markdown", "metadata": {}, "source": ["------------------\n", "* Guess the condition number of the Vandermonde matrix for $n=5,10,20$:"]}, {"cell_type": "code", "outputs": [{"output_type": "pyout", "metadata": {}, "prompt_number": 5, "text": ["686.43494181859478"]}], "collapsed": false, "input": ["n = 5\n", "\n", "V = np.array([np.linspace(0, 1, n)**i for i in range(n)]).T\n", "la.cond(V)"], "prompt_number": 5, "language": "python", "metadata": {}}, {"cell_type": "code", "outputs": [], "collapsed": false, "input": [], "language": "python", "metadata": {}}]}], "nbformat": 3}