Block Lanczos Techniques for Accelerating the Block Cimmino Method

Abstract

We consider acceleration techniques for the block Cimmino iterative method for solving general sparse systems. For iteration matrices that are not too ill conditioned, the conjugate gradient algorithm is a good method for accelerating the convergence. For ill-conditioned problems, the use of preconditioning techniques can improve the situation, but the classical conjugate gradient acceleration still performs poorly because of clusters of eigenvalues at the ends of the spectrum of the iteration matrix. We therefore try variants of the block Lanczos method, including the block conjugate gradient method. On some test examples, these techniques are convergent whereas the conjugate gradient method is not.