BLOCK LANCZOS TECHNIQUES FOR ACCELERATING THE BLOCK CIMMINO METHOD

We consider acceleration techniques for the block Cimmino iterative me thod for solving general sparse systems. For iteration matrices that a re 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 b ecause of clusters of eigenvalues at the ends of the spectrum of the i teration 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 metho d is not.