The regularizing properties of global GMRES for solving large-scale linear discrete ill-posed problems with several right-hand sides

Abstract

The global Krylov subspace iterative methods are an attractive class of iterative solvers for solving linear systems with several right-hand sides. In this paper, the global version of the GMRES method is applied to solve linear discrete ill-posed problems that arise from the discretization of linear ill-posed problems, pattern classification and dimensionality reduction. The regularizing properties of the global GMRES method are analyzed, and a regularized global GMRES method is developed for solving linear discrete ill-posed problems with multiple right-hand sides contaminated by errors. Some numerical experiments on test matrices are presented to show the efficiency of the proposed method.