The minimal-norm Gauss-Newton method and some of its regularized variants

Electronic Transactions on Numerical Analysis

article

Federica Pes¹  Giuseppe Rodriguez¹ 

[1] Department of Mathematics and Computer Science, University of Cagliari, Via Ospedale 72

关键词: nonlinear least-squares;    nonlinear inverse problem;    regularization;    Gauss-Newton method;   

DOI  :  10.1553/etna_vol53s459

学科分类：数学（综合）

来源: Kent State University * Institute of Computational Mathematics

【 摘 要 】

Nonlinear least-squares problems appear in many real-world applications. When a nonlinear model is used to reproduce the behavior of a physical system, the unknown parameters of the model can be estimated by fitting experimental observations by a least-squares approach. It is common to solve such problems by Newton's method or one of its variants such as the Gauss-Newton algorithm. In this paper, we study the computation of the minimal-norm solution to a nonlinear least-squares problem, as well as the case where the solution minimizes a suitable semi-norm. Since many important applications lead to severely ill-conditioned least-squares problems, we also consider some regularization techniques for their solution. Numerical experiments, both artificial and derived from an application in applied geophysics, illustrate the performance of the different approaches.

【 授权许可】

Unknown