A. Rieder, ADDITIVE AND MULTIPLICATIVE SCHWARZ ALGORITHMS FOR LINEAR ILL-POSED PROBLEMS, Zeitschrift fur angewandte Mathematik und Mechanik, 76, 1996, pp. 187-190
Additive and multiplicative Schwarz algorithms are described for the e
fficient iterative resolution of a linear system arising by the discre
tization and Tikhonov regularization of an ill-posed problem. The algo
rithms and their convergence analyses are presented in a rather abstra
ct framework which applies - for instance - to integral equations of t
he first kind discretized either by spline functions or Daubechies wav
elets. Numerical experiments are reported which substantiate the quali
ty of the convergence analysis.