Optimal parameters in the HSS-like methods for saddle-point problems

For the Hermitian and skew-Hermitian splitting iteration method and its accelerated variant for solving the large sparse saddle-point problems, we compute their quasi-optimal iteration parameters and the corresponding quasi-optimal convergence factors for the more practical but more difficult case that the (1, 1)-block of the saddle-point matrix is not algebraically equivalent to the identity matrix. In addition, the algebraic behaviors and the clustering properties of the eigenvalues of the preconditioned matrices with respect to these two iterations are investigated in detail, and the formulas for computing good iteration parameters are given under certain principle for optimizing the distribution of the eigenvalues. Copyright (C) 2008 John Wiley & Sons, Ltd.