TWO ALGORITHMS FOR SYMMETRIC LINEAR SYSTEMS WITH MULTIPLE RIGHT-HAND SIDES

In this paper, we investigate the block Lanczos algorithm for solving large sparse symmetric linear systems with multiple right-hand sides, and show how to incorporate deflation to drop converged linear systems using a natural convergence criterion, and present an adaptive block Lanczos algorithm. We propose also a block version of Paige and Saunders' MINRES method for iterative solution of symmetric linear systems, and describe important implementation details. We establish a relationship between the block Lanczos algorithm and block MINRES algorithm, and compare the numerical performance of the Lanczos algorithm and MINRES method for symmetric linear systems applied to a sequence of right-hand sides with that of the block Lanczos algorithm and block MINRES algorithm for multiple linear systems simultaneously.