Semi-convergence analysis of preconditioned deteriorated PSS iteration method for singular saddle point problems

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

“…If P α = αQ 1 and P β = βQ 2 , where matrices Q 1 and Q 2 are HPD matrices, then the preconditioner (13) coincides with the EPSS which we denote by P EPSS . A special case of this preconditioner is PDPSS preconditioner in [29] where C = 0 and B is a rank deficient matrix. iii.…”

“…For nonsingular generalized saddle point problem, a number of iteration methods have been developed in the literature, such as the SOR-like method [24], the GSOR method [7], the Uzawa method [13], the parametrized inexact Uzawa methods [8], the Hermitian and skew-Hermitian splitting (HSS) methods [9,39] and so on. Also, when the generalized saddle point problem ( 1) is singular, some iteration methods and preconditioning techniques have been presented, such as the generalized parametrized inexact Uzawa methods [42], HSS method [2], regularized HSS method [20], preconditioned deteriorated PSS method [29], relaxed deteriorated PSS preconditioner [28], GSS method and preconditioner [17,21,27,36], inexact version of the GSS method [26], modification of the GSS method [35], constraint preconditioning method [43,44] and so on.…”