Biography matlab code for newton method method

% Define the Objective Function

f = @(x,y) x.^3 .* exp(-x.^2 - y.^4);

% Define the Gradient Function

grad_f = @(x,y) [-3*x.^2 .* exp(-x.^2 - y.^4) + 2*x.^5 .* exp(-x.^2 - y.^4), ...

-4*y.^3 .* x.^3 .* exp(-x.^2 - y.^4)];

% Define the Hessian Function

second_grad_f = @(x, y) [ ...

-6*x.*exp(-x.^2 - y.^4) + 6*x.^4.*exp(-x.^2 - y.^4) - 4*x.^7.*exp(-x.^2 - y.^4), ...

-12*y.^3.*x.^2.*exp(-x.^2 - y.^4); ...

-12*y.^3.*x.^2.*exp(-x.^2 - y.^4), ...

-12*y.^2.*x.^3.*exp(-x.^2 - y.^4) + 16*y.^6.*x.^3.*exp(-x.^2 - y.^4) ...

starting_points = [0, 0; -1, -1; 1, 1];

fprintf('Minimization of f With Newton Method\n');

for i = 1:size(starting_points, 1)

[xk, steps, points] = newtonMethod(epsilon, starting_points(i,:), f, gamma, grad_f, second_grad_f);

fprintf('The lowest point found (%f, %f) with %f value and %d steps \n', xk(1), xk(2), f(xk(1), xk(2)), steps);

fval = double(f(points(:,1), points(: