On Steepest-Descent-Kaczmarz methods for regularizing systems of nonlinear ill-posed equations

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. Keywords. Nonlinear systems; Ill-posed equations; Regularization; Steepest descent method; Kaczmarz method. AMS Classification: 65J20, 47J06.

• Type: Journal
• Year: 2008
• Where: AMC
• Authors: A. De Cezaro, Markus Haltmeier, Antonio Leitão, Otmar Scherzer
• Keywords: AMC 2008, Convergent Regularization Method, Nonlinear Systems, Steepest Descent Method