MATLAB: Finding Jacobian matrix for Newton’s method

jacobian matrixnewton's method

I have a very basic newton's method that uses a loop and:
y = Jac(x)\(-F(x));
x = x + y;
to solve for the approximate solution.
Where x is a the initial guess in the form of a vector, F is the nonlinear function, and Jac is the jacobian matrix. Currently, I am inputting the jacobian by hand.
For example, system of equations =
2x(1) + x(2)
3x(1) + x(2)^2
=> Jac(x) =
[2, 1; 3, 2x(2)]
I was wondering if instead of solving it by hand if I could get Matlab to do it for me.

Best Answer

If you have the symbolic toolbox you can use the jacobian() function.
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