Algorithm 573: NL2SOL - An Adaptive Nonlinear Least-Squares Algorithm [E4]

@article{Dennis1981Algorithm5N,
  title={Algorithm 573: NL2SOL - An Adaptive Nonlinear Least-Squares Algorithm [E4]},
  author={John E. Dennis and David M. Gay and Roy E. Welsch},
  journal={ACM Trans. Math. Softw.},
  year={1981},
  volume={7},
  pages={369-383}
}
Reference [ 1] explains the algorithm realized by NL2SOL in detail. The algorithm amounts to a variation on Newton's method in which part of the Hessian matrix is computed exactly and part is approximated by a secant (quasi-Newton) updating method. Once the iterates come sufficiently close to a local solution, they usually converge quite rapidly. To promote convergence from poor starting guesses, NL2SOL uses a model/trust-region technique along with an adaptive