On Steepest-Descent-Kaczmarz Methods for Regularizing Systems of Nonlinear Ill-posed Equations

TL;DR

This paper introduces a modified steepest descent method combined with a loping Kaczmarz strategy to effectively regularize and solve nonlinear ill-posed operator equations, demonstrating convergence and practical effectiveness.

Contribution

It presents a novel regularization approach that integrates steepest descent with a loping Kaczmarz strategy for nonlinear ill-posed problems, with proven convergence.

Findings

Method is a convergent regularization technique.

Numerical tests confirm effectiveness for photoacoustic tomography.

Successful application to semiconductor device testing.

Abstract

We investigate modified steepest descent methods coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization method. Numerical tests are presented for a linear problem related to photoacoustic tomography and a non-linear problem related to the testing of semiconductor devices.