implement the multidimensional newton method for computing f(x) = 0 (with x, 0 r n ) in a matlab function mynewton with the jacobian not given in matlab

main.m
function [x, info] = mynewton(f, x0, tol, maxiter)
% Implementation of the Multidimensional Newton Method
% to solve f(x) = 0, with x, 0 r n
% Where f is a MATLAB function that returns the value of the function and the Jacobian at x
% x0 is the initial guess for x
% tol is the tolerance for the stopping criteria
% maxiter is the maximum number of iterations allowed

x = x0;
fx = f(x);
info(1) = norm(fx);
iter = 1;

while (norm(fx) > tol) && (iter < maxiter)
    J = zeros(length(x));
    h = 1e-8;

    % Approximate the Jacobian using finite differences
    for i = 1:length(x)
        xplus = x;
        xminus = x;
        xplus(i) = x(i) + h;
        xminus(i) = x(i) - h;
        fxplus = f(xplus);
        fxminus = f(xminus);
        J(:, i) = (fxplus - fxminus) / (2*h);
    end

    % Solve for the increment delta_x
    delta_x = -J \ fx;

    % Update x and fx
    x = x + delta_x;
    fx = f(x);

    % Update iteration count and residual info
    iter = iter + 1;
    info(iter) = norm(fx);
end

if iter == maxiter
    fprintf('Maximum number of iterations reached \n');
end

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