An inexact relaxed DPSS preconditioner for saddle point problem

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

“…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.…”

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].…”

Positive Definite and Semi-Definite Splitting Methods for Non-Hermitian Positive Definite Linear Systems

“…Let D = diag(a 11 , a 22 The linear system has many important practical applications, such as diffuse optical tomography, molecular scattering, lattice quantum chromodynamics (see, e.g., [1,7,8,22,24,38,39,41]). Many researchers have been devoted themselves to the numerical solution of (1.1) (see e.g., [2-4, 10, 11, 18, 21, 25, 27, 28, 36, 37, 40, 42, 45-47] and the references therein) and proposed kinds of available iteration methods for solving the system (1.1), in which splitting iteration methods (see e.g., [9,[13][14][15][16][17]19,[29][30][31]35,44]) and Krylov subspace methods (see e.g., [5,20,23,26,32,43]) attract a lot of attention. In [16], the authors presented a Hermitian and skew-Hermitian splitting (HSS) iteration method for solving (1.1) and showed that the HSS method converges unconditionally to the unique solution of the system.…”