Inexact Gauss-Newton methods with matrix approximation by sampling for nonlinear least-squares and systems

2023/10/09 by Stefania Bellavia, Bellavia, Stefania, Greta Malaspina +3 · 1 citation
Engineering · Environmental Science · Mathematics · #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Soil Geostatistics and Mapping #Sparse and Compressive Sensing Techniques #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.2310.05501

openalex publication_date 2023/10/09 · openalex created_date 2023/10/12 · openalex updated_date 2026/07/28

Abstract

We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and for nonlinear systems ofequations. Random models are formed using suitable sampling strategies for the matrices involved in the deterministic models. The analysis of the expected number of iterations needed in the worst case to achieve a desired level of accuracy in the first-order optimality condition provides guidelines for applying sampling and enforcing, with \minora fixed probability, a suitable accuracy in the random approximations. Results of the numerical validation of the algorithms are presented.

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