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38 lines
1.1 KiB
Matlab
38 lines
1.1 KiB
Matlab
function [x, i] = SecantMethod(f, x0, x1, tol, max_iter)
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% solves f(x) = 0 by doing max_iter steps of the secant method;
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% the secant method requires two initial values, x0 and x1
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% which should ideally be chosen close to the root;
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% y = feval(f, x) evaluates a function using its name or its handle
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% and using the input arguments;
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for i = 1 : max_iter
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% function values: f(x0) and f(x1)
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f0 = feval(f, x0);
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f1 = feval(f, x1);
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% the root of function f is approximated using the formula
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xi = x1 - f1 * (x1 - x0) / (f1 - f0);
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% calculate f(xi)
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fxi = feval(f, xi);
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% xi is the solution
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if abs(fxi) < eps
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x = xi;
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return;
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endif
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% calculate eps
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epsilon = abs((xi - x1) / xi);
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% stop if the secant method reached its convergence limit
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if epsilon < tol
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x = xi;
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return;
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endif
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% update the last two computed values
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x0 = x1;
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x1 = xi;
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endfor
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disp('Maximum number of iterations reached');
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endfunction
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