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37 lines
997 B
Matlab
37 lines
997 B
Matlab
function [x, i] = BisectionMethod(f, a, b, tol, max_iter)
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% solves the equation f(x) = 0 for the real variable x
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% in i steps from the total number of iterations max_iter;
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% the method requires a continuous function f;
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% the function is defined on a given interval [a, b];
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% f(a) and f(b) have opposite signs;
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for i = 1 : max_iter
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% calculate the midpoint
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x = (a + b) / 2;
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fact = feval(f, a) * feval(f, x);
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% if the product is negative, the root is in
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% between a and x
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if fact < 0
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b = x;
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% if the product is positive, the root is in
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% between b and x
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elseif fact > 0
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a = x;
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% if the product is null, the root is found
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else
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return;
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endif
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% if the root is unknown, the new midpoint is calculated
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new_x = (a + b) / 2;
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% if the relative absolute error is lower than the given tolerance,
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% then the bisection method reached convergence limit
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err = abs((new_x - x) / new_x);
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if err < tol
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x = new_x;
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return;
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endif
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endfor
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endfunction
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