Processing math: 100%

2015年11月12日木曜日

学習環境

  • 数式入力ソフト(TeX, MathML): MathType
  • MathML対応ブラウザ: Firefox、Safari
  • MathML非対応ブラウザ(Internet Explorer, Google Chrome...)用JavaScript Library: MathJax

オイラーの贈物―人類の至宝eiπ=-1を学ぶ (吉田 武(著)、東海大学出版会)の第Ⅰ部(基礎理論(Basic Theory))、3章(微分(Differentiation))、3.8(関数のグラフを描く)、問題5.を解いてみる。

問題5.

f(x)=x3+x24x+1f(1)(x)=3x2+2x4=13(x+3)27f(1)(x)=0x=1±133f(2)(x)=6x+2=6(x+13)f(2)(x)=0x=131133<13<1+133f(13)=127+19+43+1=1+3+36+2727=6527f(1+133)=1+31339+131327+142139+44133+1=40+1613+42613+363613+2727=65261327<0f(1133)=65+261327xn+1=xnf(xn)f(1)(xn)=xnx3n+xn24xn+13x2n+2xn4=2x3n+x2n13x2n+2xn453<1133x0=53x1=25027+25912531034=250+752727=20227(=7.481···)python使x2=-154027912931876(=-5.253561542166176)x3=-3319063268830266108581860558640294071840166(=-3.856870541321936)x4=-3.0647804042831877x5=-2.7248676719102827x6=-2.654106846739904x7=-2.6510987533831787x8=-2.651093408954031x9=-2.651093408937175

コード(Emacs)

#!/usr/bin/env python3
# -*- coding: utf-8 -*_

import fractions

def newton(x, r=10):
    inner = lambda x:fractions.Fraction(2 * x ** 3 + x ** 2 - 1,
                                        3 * x ** 2 + 2 * x - 4)
    for i in range(r):
        print('x_{0} = {1}'.format(i, float(x)))
        x = inner(x)
    print()

x = fractions.Fraction(-5, 3)
newton(x)

x = 0
newton(x)

x = fractions.Fraction(5, 3)
newton(x)

入出力結果(Terminal, IPython)

$ ./sample5.py
x_0 = -1.6666666666666667
x_1 = -7.481481481481482
x_2 = -5.253561542166176
x_3 = -3.856870541321936
x_4 = -3.0647804042831877
x_5 = -2.7248676719102827
x_6 = -2.654106846739904
x_7 = -2.6510987533831787
x_8 = -2.651093408954031
x_9 = -2.651093408937175

x_0 = 0.0
x_1 = 0.25
x_2 = 0.27358490566037735
x_3 = 0.2738905022655762
x_4 = 0.27389055496421605
x_5 = 0.2738905549642176
x_6 = 0.2738905549642176
x_7 = 0.2738905549642176
x_8 = 0.2738905549642176
x_9 = 0.2738905549642176

x_0 = 1.6666666666666667
x_1 = 1.4396135265700483
x_2 = 1.3812200268652726
x_3 = 1.3772213440738694
x_4 = 1.3772028543676846
x_5 = 1.3772028539729577
x_6 = 1.3772028539729577
x_7 = 1.3772028539729577
x_8 = 1.3772028539729577
x_9 = 1.3772028539729577

$

0 コメント:

コメントを投稿