File:Brent method example.png

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

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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');