Shift-splitting preconditioners for saddle point problems

A modified positive-definite and skew-Hermitian splitting preconditioner for generalized saddle point problems from the Navier-Stokes equation

“…From the numerical examples in [42], we find the eigenvalues distribution of the preconditioned matrix P −1 GSS A gather more closely than those in [41], also the convergence performance is better.…”

“…Cao et al, in [41], proposed the following shift-splitting preconditioner for solving the classical saddle point problem:…”

“…So, a good preconditioner must be given as close as possible to the coefficient matrix. The preconditioners for saddle problems mainly can be considered in these cases, such as, block triangular preconditioners [2,22], block diagonal preconditioners [23][24][25], fully factorized two-by-two block matrix precoditioners [26,27], etc., see [28][29][30][31][32][33][34][35][36][37][38][39][40] for more detailed investigations.…”

An extension of the positive-definite and skew-Hermitian splitting method for preconditioning of generalized saddle point problems

“…(a) When A is HPD, the P SS preconditioner was studied in [15] and P GSS preconditioner is studied in [21,32,34]. Moreover the P ESS preconditioner was presented in [45].…”

A modified product preconditioner for indefinite and asymmetric generalized saddle-point matrices

“…In recent years, many authors pay more attention to preconditioned iterative methods [7][8][9][10][15][16][17][18][19][20]34,35] for solving large sparse linear systems in terms of lower requirement for storage and fast convergence. A large amount of work has been devoted to studying preconditioners, such as, block diagonal preconditioner (BD) [12,13], block triangular preconditioner (BT) [11,14,22,23,25] , constraint preconditioner (CP) [21,24,[26][27][28] and product preconditioner (PP) [23,29].…”