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File:Brent method example.png

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Original file(932 × 735 pixels, file size: 8 KB, MIME type: image/png)

Summary

Graph of (x + 3)(x − 1)2, used to illustrate Brent's method. Created by Jitse Niesen in Matlab.

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.

Matlab code

f = @(x) (x+3).*(x-1).^2;
xs = linspace(-5,2.5);
ys = f(xs);

% x-axis
clf; hold on;
plot([-5 3], [0 0], 'k');
for k = -4:2
  if k ~= 0
    plot([k k], [0.7 -0.7], 'k');
    text(k, -1, int2str(k), 'HorizontalAlignment', 'center', ...
         'VerticalAlignment', 'top', 'FontSize', 12);
  end;
end;

% y-axis
plot([0 0], [-35 15], 'k');
for k = -30:5:10
  if k ~= 0
    plot([0.1 -0.1], [k k], 'k');
    text(-0.15, k, int2str(k), 'HorizontalAlignment', 'right', ...
         'VerticalAlignment', 'middle', 'FontSize', 12);
  end;
end;

% graph
plot(xs,ys, 'Linewidth',3);
axis([-4.5 2.1 -31 11]);
axis off;
print -dpng 'brent_tmp.png';
system('convert -trim +repage brent_tmp.png brent.png');

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Date/TimeThumbnailDimensionsUserComment
current09:21, 17 June 2006Thumbnail for version as of 09:21, 17 June 2006932 × 735 (8 KB)Jitse Niesenremove offset
09:03, 17 June 2006Thumbnail for version as of 09:03, 17 June 2006932 × 735 (8 KB)Jitse NiesenGraph of (''x'' + 3)(''x'' − 1)<sup>2</sup>, used to illustrate w:en:Brent's method. Created by ~~~ in Matlab.
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