secant method in matlab

main.m
function [x, fx, n] = secant_method(f, x0, x1, tol, maxiter)
% SECANT_METHOD finds a root of f using the secant method
% Inputs:
%   f: the function to find the root of
%   x0, x1: initial guesses for the root
%   tol: the tolerance for the root
%   maxiter: the maximum number of iterations allowed
% Outputs:
%   x: the estimated root of f
%   fx: the value of f at x
%   n: the number of iterations used

% Initialize values
n = 0;          % number of iterations
err = tol + 1;  % initialize error

while (err > tol) && (n < maxiter)
    % calculate the slope of the secant line
    slope = (f(x1) - f(x0)) / (x1 - x0);
    
    % update the estimate of the root
    x = x1 - f(x1) / slope;
    
    % update error and check for convergence
    err = abs(x - x1);
    
    % move guesses closer to the root
    x0 = x1;
    x1 = x;
    
    % increment iteration counter
    n = n + 1;
end

% return the root and corresponding function value
fx = f(x);
end
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main.m
f = @(x) x^3 - 6*x^2 + 11*x - 6.1;
[x, fx, n] = secant_method(f, 0.5, 1.5, 1e-6, 100);
disp(['The root is x = ' num2str(x) ' after ' num2str(n) ' iterations.'])
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main.m
The root is x = 2.4291 after 15 iterations.
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