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.