Secant

function secant_method()
    f = @(x) x^2 - 9;
    eps = 1e-6;
    x0 = 1000;  x1 = x0 - 1;
    [solution,no_iterations] = secant(f, x0, x1, eps);
    if no_iterations > 0   % Solution found
        fprintf('Number of function calls: %d\n', 2 + no_iterations);
        fprintf('A solution is: %f\n', solution)
    else
        fprintf('Abort execution.\n')
    end
end

function [solution,no_iterations] = secant(f, x0, x1, eps)
    f_x0 = f(x0);
    f_x1 = f(x1);
    iteration_counter = 0;
    while abs(f_x1) > eps && iteration_counter < 100
        try
            denominator = (f_x1 - f_x0)/(x1 - x0);
            x = x1 - (f_x1)/denominator;
        catch
            fprintf('Error! - denominator zero for x = \n', x1)
            break
        end
        x0 = x1;
        x1 = x;
        f_x0 = f_x1;
        f_x1 = f(x1);
        iteration_counter = iteration_counter + 1;
    end
    % Here, either a solution is found, or too many iterations
    if abs(f_x1) > eps
        iteration_counter = -1;
    end
    solution = x1;
    no_iterations = iteration_counter;
end