newton method with jacobian in matlab

To use the Newton method with Jacobian in MATLAB, you can follow these steps:

1. Define the function that you want to optimize using the Newton method. Let's call this function fun.

main.m
function F = fun(x)
    F = [2*x(1)^2 + x(2)^2 - 4; 
         x(1)^2 - x(2) - 1];
end
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2. Define the Jacobian matrix of the function fun.

main.m
function J = jacobian(x)
    J = [4*x(1) 2*x(2); 
         2*x(1) -1];
end
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3. Choose an initial guess for the solution x0.

main.m
x0 = [1; 1];
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4. Set the maximum number of iterations for the Newton method algorithm.

main.m
max_iter = 20;
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5. Set the tolerance for convergence of the algorithm.

main.m
tol = 1e-6;
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6. Implement the Newton method algorithm with the Jacobian matrix in a loop.

main.m
iter = 1;
x = x0;
while iter <= max_iter
    F = fun(x);
    J = jacobian(x);
    delta_x = -J\F;
    x = x + delta_x;
    if norm(delta_x) < tol
        break
    end
    iter = iter + 1;
end
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7. Display the solution x.

main.m
disp(x);
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That's it! You can use this code template to apply the Newton method with Jacobian in MATLAB for your own functions.