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Summary edit

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

Licensing edit

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 edit

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');