A generalized preconditioned HSS method for singular saddle point problems

On semi-convergence of the Uzawa–HSS method for singular saddle-point problems

“…We call (1.1) the singular saddle-point problem. A number of effective methods have been proposed in the literature to solve the singular saddle-point problems, such as the Uzawa-type methods [8][9][10][11], Krylov subspace methods [12,13] and matrix splitting iteration methods [14][15][16][17][18] Based on the above splitting, Bai et al [19] proposed an HSS iteration method for solving non-Hermitian positive definite system of linear equations. The iteration scheme of the HSS method used for solving Au ¼ q can be written as ðaI þ HÞu ðkþ1=2Þ ¼ ðaI À SÞu ðkÞ þ q; ðaI þ SÞu ðkþ1Þ ¼ ðaI À HÞu ðkþ1=2Þ þ q; where a is a positive iteration parameter and TðaÞ ¼ ðaI þ SÞ À1 ðaI À HÞðaI þ HÞ À1 ðaI À SÞ ¼ ðaI þ SÞ À1 ðaI þ HÞ À1 ðaI À HÞðaI À SÞ;…”

General constraint preconditioning iteration method for singular saddle-point problems

“…The linear systems (1.1) are called as singular saddle-point problems. Some authors have studied iterative methods or preconditioners for this kind of singular problems and obtained many important and interesting results; see [3,4,16,17,18,19,20]. Owing to the singularity of matrix M , iteration scheme (1.3) can not be used to solve singular saddle-point problems (1.1).…”

On semi-convergence of a class of relaxation methods for singular saddle point problems

“…We call (1.1) the singular saddle point problem. A number of effective methods have been proposed in the literature to solve the singular saddle point problems, such as the Uzawa-type methods [22,32,35], Krylov subspace methods [26,33] and matrix splitting iteration methods [13,14,17].…”