{"metadata": {"name": "", "signature": "sha256:ef7f191484e89ea2bc8dec9dd0d4d114493244a22f532ca653d8c0d58ec96155"}, "worksheets": [{"metadata": {}, "cells": [{"metadata": {}, "source": ["# Newton's Method"], "cell_type": "markdown"}, {"language": "python", "input": ["import numpy as np\n", "import matplotlib.pyplot as pt"], "prompt_number": 85, "metadata": {}, "outputs": [], "collapsed": false, "cell_type": "code"}, {"metadata": {}, "source": ["Here's a function:"], "cell_type": "markdown"}, {"language": "python", "input": ["def f(x):\n", " return x**3 - x +1\n", "\n", "def df(x):\n", " return 3*x**2 - 1\n", "\n", "xmesh = np.linspace(-2, 2, 100)\n", "pt.ylim([-3, 10])\n", "pt.plot(xmesh, f(xmesh))"], "prompt_number": 86, "metadata": {}, "outputs": [{"metadata": {}, "text": ["[]"], "output_type": "pyout", "prompt_number": 86}, {"metadata": {}, "text": [""], "output_type": "display_data", "png": 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"collapsed": false, "cell_type": "code"}, {"language": "python", "input": ["guesses = [2]"], "prompt_number": 87, "metadata": {}, "outputs": [], "collapsed": false, "cell_type": "code"}, {"metadata": {}, "source": ["Evaluate this cell many times in-place (using Ctrl-Enter)"], "cell_type": "markdown"}, {"language": "python", "input": ["x = guesses[-1] # grab last guess\n", "\n", "slope = df(x)\n", "\n", "# plot approximate function\n", "pt.plot(xmesh, f(xmesh))\n", "pt.plot(xmesh, f(x) + slope*(xmesh-x))\n", "pt.plot(x, f(x), \"o\")\n", "pt.ylim([-3, 10])\n", "pt.axhline(0, color=\"black\")\n", "\n", "# Compute approximate root\n", "xnew = x - f(x) / slope\n", "guesses.append(xnew)\n", "print(xnew)"], "prompt_number": 84, "metadata": {}, "outputs": [{"text": ["-1.324717957244746\n"], "output_type": "stream", "stream": "stdout"}, {"metadata": {}, "text": [""], "output_type": "display_data", "png": 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