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

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

2008-01-20

arxiv.org/abs/0801.3088v3

Applied Mathematics and Computation 202 (2008), pp. 596-607

Mathematics

Numerical Analysis

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

Scientific paper

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.

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