On hybrid preconditioning methods for large sparse saddle-point problems

Based on the block-triangular product approximation to a 2-by-2 block matrix, a class of hybrid preconditioning methods is designed for accelerating the MINRES method for solving saddle-point problems. The appropriate values for the parameters involved in the new preconditioners are estimated, so that the numerical conditioning and the spectral property of the saddle-point matrix of the linear system can be substantially improved. Several practical hybrid preconditioners and the corresponding preconditioning iterative methods are constructed and studied, too. (C) 2010 Elsevier Inc. All rights reserved.