Function gaussNewton

Performs Gauss-Newton optimization for nonlinear least squares problems.

Algorithm:

1. Start with initial parameters
2. Compute residual vector r and Jacobian matrix J
3. Solve normal equations: (J^T J) δ = -J^T r
4. Update parameters: x_new = x_old + δ
5. Repeat until convergence

The Gauss-Newton method approximates the Hessian as J^T J, which is exact for linear least squares and a good approximation for nonlinear cases.