Regularized Iterative Method for Ill-posed Linear Systems Based on Matrix Splitting

Abstract

In this paper, the concept of matrix splitting is introduced to solve a large sparse ill-posed linear system via Tikhonov’s regularization. In the regularization process, we convert the ill-posed system to a well-posed system. The convergence of such a well-posed system is discussed by using different types of matrix splittings. Comparison analysis of both systems are studied by operating certain types of weak splittings. Further, we have extended the  double splitting of [Song J. and Song Y, Calcolo 48(3), 245–260, 2011]  to double weak splitting of type II for nonsingular symmetric matrices. In addition to that, some more comparison results are presented with the help of such weak double splittings of type I and type II.