Deflated Shifted Block Krylov Subspace Methods for Hermitian Positive Definite Matrices

Abstract

This thesis considers the task of computing solutions of families of large sparse linear systems that differ by a shift with the identity matrix and have several different right-hand sides at the same time. We explore the applicability of existing Krylov subspace methods for solving shifted systems and methods for solving systems with multiple right-hand sides. Moreover, we develop methods that, based on deflated block Lanczos-Type processes, exploit both features---shifts and multiple right-hand sides---at once and tackle well-known problems that multiple right-hand sides can bring along. We present numerical evidence that our methods can be superior as compared to applying other iterative methods, in typical situations.