File:Secant method example code result.svg
Summary
| Description |
English: Example of finding the root of the function represented by the red line (cos(x) − x3) using the secant method, with the increasingly accurate approximations represented by the blue straight lines. |
| Date | |
| Source | Intended to replace bitmap graph en:Image:Secantmethod_jaredwf.png, with straight line equations derived from example program on article. |
| Author | Qef |
| Other versions | Original bitmap version: http://en.wikipedia.org/wiki/Image:Secantmethod_jaredwf.png |
Source code
Created with Gnuplot using the following input file:
set terminal svg font "Bitstream Vera Sans,12"
set output "Secant_method_example_code_result.svg"
set xrange [0:1]
set yrange [-0.5:3]
set xzeroaxis linetype -1
set yzeroaxis linetype -1
set xtics axis nomirror offset 0,0.3
set ytics axis nomirror offset -0.8
set key off
set border 0
plot -1.4596976941*x + 1.0000000000 with line lt rgbcolor "blue" lw 0.3, \
-2.8976523576*x + 2.4379546634 with line lt rgbcolor "blue" lw 0.4, \
-2.4441383687*x + 2.1272643125 with line lt rgbcolor "blue" lw 0.5, \
-2.9527747549*x + 2.5552081431 with line lt rgbcolor "blue" lw 0.6, \
-3.0224715585*x + 2.6158689981 with line lt rgbcolor "blue" lw 0.7, \
-3.0081989720*x + 2.6035180968 with line lt rgbcolor "blue" lw 0.8, \
-3.0085369652*x + 2.6038106210 with line lt rgbcolor "blue" lw 0.9, \
-3.0085385603*x + 2.6038120015 with line lt rgbcolor "blue" lw 1.0, \
cos(x) - x*x*x with line linetype rgbcolor "red" linewidth 2
The series of line equations for the straight blue lines were produced by the example program in the Wikipedia:Secant method article, by adding the following lines to the start of the loop in the SecantMethod function:
double g = (f(xn) - f(xn_1)) / (xn - xn_1);
printf("%.10f*x + %.10f\n", g, f(xn) - (g * xn));
The SVG was filtered with the following command to change the hyphen in a label to a proper minus sign:
sed -i 's/<text>-/<text>\xE2\x88\x92/g' Secant_method_example_code_result.svg
Licensing
 |
This work has been released into the public domain by its author, Qef. This applies worldwide. In some countries this may not be legally possible; if so: |
