To use the Newton method to solve a system of nonlinear equations in MATLAB, one needs to compute the Jacobian of the system.

Here is an example implementation of the Newton method in MATLAB, where `F`

is the system of nonlinear equations, `J`

is the Jacobian of `F`

, `x0`

is the initial guess, `tol`

is the tolerance for the solution, and `max_iter`

is the maximum number of iterations:

`main.m200 chars11 lines`

To use this function, one needs to provide the function handle `F`

, the function handle `J`

, the initial guess `x0`

, the tolerance `tol`

, and the maximum number of iterations `max_iter`

.

For example, if we want to solve the system of equations `sin(x) + y^2 = 0`

, `x^2 + y = 1`

, we can define the function handles as follows:

main.m91 chars3 lines

Then we can call the `newton`

function as follows:

main.m169 chars5 lines

After running this code, the solution `x`

and the number of iterations `iter`

will be returned.

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