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

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.

22 pages (8 figures). For this version we have corrected some typos and also have corrected Equation (25) in the proof of Theorem 3.3

References in corpus (2)

• Regularization of systems of nonlinear ill-posed equations: I. Convergence Analysis
• On inverse problems for semiconductor equations