eleminating jacobian from newton method in matlab

To eliminate the use of the Jacobian matrix in the Newton method in MATLAB, one can use the built-in optimization function `fsolve`. `fsolve` allows you to find the roots of a system of nonlinear equations without explicitly calculating the Jacobian matrix.

Here is an example of how to use `fsolve` to solve a system of nonlinear equations:

```main.m```% Define the function
f = @(x) [x(1)^2 + x(2)^2 - 1;
x(1)^2 - x(2)];

% Set initial guess
x0 = [1; 1];

% Solve for the roots
x = fsolve(f, x0);

% Display results
disp(x);
```184 chars13 lines```

In this example, we define a function `f` that takes a vector `x` and returns a vector of values that must be equal to zero in order to find a root. We set an initial guess `x0` for the root and use `fsolve` to solve for it. Finally, we display the result.

Note that `fsolve` uses an iterative method similar to the Newton method, but it does not require the user to explicitly calculate the Jacobian matrix.

related categories

gistlibby LogSnag