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Summary

DescriptionLaplaces method.png	English: Illustration of the method of steepest descent
Date	23 May 2009, 21:00 (UTC)
Source	self-made with Matlab
Author	Oleg Alexandrov
Permission (Reusing this file)	Public domain

This diagram was created with MATLAB.

Category:PNG created with MATLAB#Laplaces%20method.png

Source code

% Illustration of Laplace's method

N   = 500;
L   = 15;
fs  = 12;
lw  = 2;
lw2 = 1;

X = linspace(-L, L, N)+eps;
f = sin(X)./X;
g = (1-X.^2/6);

figure(1); clf; hold on;
q = 1.01;

subplot(2, 3, 1);
set(gca, 'fontsize', fs);
set(gca, 'LineWidth', lw2);
hold on;
M = 0.5;
Y = exp(M*f);
Z = exp(M*g);
plot(X, Z, 'r', 'linewidth', lw);
plot(X, Y, 'b', 'linewidth', lw);
R = max(Z);
axis([-L, L, 0, q*R]);

subplot(2, 3, 4);
set(gca, 'fontsize', fs);
set(gca, 'LineWidth', lw2);
hold on;
M = 3;
Y = exp(M*f);
Z = exp(M*g);
plot(X, Z, 'r', 'linewidth', lw);
plot(X, Y, 'b', 'linewidth', lw);
R = max(Z);
axis([-L, L, 0, q*R]);

saveas(gcf, 'Laplaces_method.eps', 'psc2');

% Converted from eps to png with the formula
% convert -antialias -density 200 Laplaces_method.eps Laplaces_method.png

Licensing

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.

Category:Self-published work#Laplaces%20method.png Category:PD-self#Laplaces%20method.png Category:Numerical analysis Category:Files by User:Oleg Alexandrov from en.wikipedia Category:Images with Matlab source code