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. 
A. De Cezaro, M. Haltmeier, A. Leitao, O. Scherzer