On Steepest-Descent-Kaczmarz Methods for Regularizing Systems of Nonlinear Ill-posed Equations
Provides a convergent regularization method for nonlinear ill-posed problems, but the results are incremental and limited to specific test cases.
The paper proposes a modified steepest descent method with a loping Kaczmarz strategy for regularizing nonlinear ill-posed systems, proving convergence as a regularization method. Numerical tests on photoacoustic tomography and semiconductor device testing demonstrate applicability.
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.