# 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
```86 chars5 lines```
1. 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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1. Choose an initial guess for the solution `x0`.
```main.m```x0 = [1; 1];
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1. Set the maximum number of iterations for the Newton method algorithm.
```main.m```max_iter = 20;
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1. Set the tolerance for convergence of the algorithm.
```main.m```tol = 1e-6;
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1. 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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1. 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.

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