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File:NewtonsMethodConvergenceFailure.svg

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Original file (SVG file, nominally 1,000 × 1,000 pixels, file size: 84 KB)

Summary

Description Plot of x^3 - 2x + 2, including tangent lines at x = 0 and x = 1. Illustrates why Newton's method doesn't always converge for this function.
Date
Source Self-made, created using FooPlot and modified in Inkscape.
Author Aaron Rotenberg

Gnuplot

# Author: Ika, 24 Aug 2013

set terminal svg size 1000 1000 fixed enhanced fname 'Times'  fsize 36
set output "Newton_Method_SVG.svg"

set samples 2000

set autoscale fix
set xrange [-3:4]
set yrange [-3:4]

set grid
set xtics -3,1,4
set ytics -3,1,4
set xzeroaxis linewidth 2.5
set yzeroaxis linewidth 2.5

set nokey

unset border
set multiplot
plot x lw 2 lc rgb "red"
plot -2*x+2 lw 2 lc rgb "blue"
plot x*x*x-2*x+2 lw 2 lc rgb "black"
unset multiplot

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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14 March 2008

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Date/TimeThumbnailDimensionsUserComment
current05:59, 25 August 2013Thumbnail for version as of 05:59, 25 August 20131,000 × 1,000 (84 KB)IkamusumeFan1. Much clearer labels; 2. Source code added.
00:45, 15 March 2008Thumbnail for version as of 00:45, 15 March 2008500 × 300 (6 KB)Aaron Rotenberg{{Information |Description=Plot of ''x''^3 - 2''x'' + 2, including tangent lines at ''x'' = 0 and ''x'' = 1. Illustrates why Newton's method doesn't always converge for this function. |Source=self-made |Date=March 14, 2008 |Author=

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