The Regularized Block GMERR Method and Its Simpler Version for Solving Large-Scale Linear Discrete Ill-Posed Problems

Based on the block Arnoldi process and minimizing the Frobenius norm of the error, the block generalized minimal error (GMERR) method and its simpler version are proposed for solving large-scale linear systems of equations with multiple right-hand sides. However, little is known about the behavior of these methods when they are applied to the solution of linear discrete ill-posed problems with multiple right-hand sides contaminated by errors. In this paper, the regularizing properties of the block GMERR method and the simpler block GMERR method are examined. Both a regularized block GMERR method and a regularized simpler block GMERR method are developed for solving large-scale linear discrete ill-posed problems with multiple right-hand sides. Numerical experiments on typical test matrices show the efficiency of the proposed methods.