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. Key words: symmetric linear systems, multiple right-hand sides, block Lanczos algorithm, block MINRES method AMS(MOS) subject classification: 65F10, 65F15 1 The research sup..