) implement the multidimensional newton method for computing f(x) = 0 (with x, 0 r n ) in a matlab function mynewton with the jacobian matrix in matlab

main.m
function [x, conv] = mynewton(f,J,x0,tol,maxIt)
%MYNEWTON Multidimensional Newton's method
%   [X, CONV] = MYNEWTON(F, J, X0, TOL, MAXIT) finds a zero of function
%   'f' near initial guess 'x0' using Newton's method with the Jacobian
%   matrix 'J'. It returns the zero found in 'x' and a flag 'conv'
%   indicating convergence (1) or divergence (0).
%   
%   Inputs:
%   f:   handle to multidimensional function f(x)
%   J:   handle to Jacobian matrix J(x)
%   x0:  initial guess for the root of f(x)=0
%   tol: tolerance for convergence
%   maxIt: maximum number of iterations to be executed
%  
%   Outputs:
%   x: n-dimensional vector representing the root of f(x)=0
%   conv: convergence flag (1=converged, 0=diverged)
%
%   Example usage:
%   f = @(x) [x(1)^2+x(2)^2-1; x(1)+x(2)-0.4];
%   J = @(x) [2*x(1), 2*x(2); 1, 1];
%   x0 = [0;0];
%   tol = 1e-6;
%   maxIt = 50;
%   [x, conv] = mynewton(f, J, x0, tol, maxIt);

conv = 0; % assuming divergence
for i=1:maxIt
    fx = f(x0);
    if norm(fx) < tol
        conv = 1; % converged
        break;
    end
    Jx = J(x0);
    s = -Jx\fx; % solve using the backslash operator
    x0 = x0 + s;
end
x = x0;

end
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