BLOCK LANCZOS TECHNIQUES FOR ACCELERATING THE BLOCK CIMMINO METHOD

Citation
M. Arioli et al., BLOCK LANCZOS TECHNIQUES FOR ACCELERATING THE BLOCK CIMMINO METHOD, SIAM journal on scientific computing, 16(6), 1995, pp. 1478-1511
Citations number
27
Categorie Soggetti
Computer Sciences",Mathematics
ISSN journal
10648275
Volume
16
Issue
6
Year of publication
1995
Pages
1478 - 1511
Database
ISI
SICI code
1064-8275(1995)16:6<1478:BLTFAT>2.0.ZU;2-A
Abstract
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.