Greedy Kaczmarz methods for nonlinear equation

Abstract

A class of randomized Kaczmarz methods for solving nonlinear systems of equations was introduced by Q. Wang and W. Li. These methods significantly reduce computational and storage requirements by computing only a single row of the Jacobian matrix in each iteration, rather than the entire matrix. Building upon this approach and the greedy randomized Kaczmarz method for linear systems, we propose two novel methods for solving overdetermined or singular nonlinear systems: the nonlinear greedy deterministic Kaczmarz (NGDK) method and the nonlinear greedy randomized Kaczmarz (NGRK) method. This paper presents the local convergence analysis and numerical experiments for the proposed methods. The experimental results demonstrate the efficacy of these methods in the case of noise-free data.