A doubly relaxed minimal-norm Gauss-Newton method for underdetermined nonlinear least-squares problems
Numerical Analysis
2021-09-20 v5 Numerical Analysis
Abstract
When a physical system is modeled by a nonlinear function, the unknown parameters can be estimated by fitting experimental observations by a least-squares approach. Newton's method and its variants are often used to solve problems of this type. In this paper, we are concerned with the computation of the minimal-norm solution of an underdetermined nonlinear least-squares problem. We present a Gauss-Newton type method, which relies on two relaxation parameters to ensure convergence, and which incorporates a procedure to dynamically estimate the two parameters, as well as the rank of the Jacobian matrix, along the iterations. Numerical results are presented.
Keywords
Cite
@article{arxiv.2101.07560,
title = {A doubly relaxed minimal-norm Gauss-Newton method for underdetermined nonlinear least-squares problems},
author = {Federica Pes and Giuseppe Rodriguez},
journal= {arXiv preprint arXiv:2101.07560},
year = {2021}
}