Based on the work of Wang and Li [A new preconditioned AOR iterative method for L-matrices, J. Comput. Appl. Math. 229 (2009) 47-53], in this paper, a new preconditioner for the AOR method is proposed for solving linear systems whose coefficient matrix is an L-matrix. Several comparison theorems are shown for the proposed method with two preconditioners. It follows from the comparison results t...

This paper looks at the SSOR algorithm and shows that, under certain conditions, we can generate an approximation to the SSOR preconditioner using only one triangular solve. We show that this approximation can result in slightly increased iterations to convergence, but increased solution eeciency when used as a preconditioner for non-symmetric, indeenite systems of equations. The paper analyzes...

The preconditioner for parameterized inexact Uzawa methods have been used to solve some indefinite saddle point problems. Firstly, we modify the preconditioner by making it more generalized, then we use theoretical analyses to show that the iteration method converges under certain conditions. Moreover, we discuss the optimal parameter and matrices based on these conditions. Finally, we propose ...

The preconditioned conjugate gradient (CG) is often applied in image reconstruction as a regularizing method. When the blurring matrix has Toeplitz structure, the modified circulant preconditioner and the inverse Toeplitz preconditioner have been shown to be effective. We introduce here a preconditioner for symmetric positive definite Toeplitz matrices based on a trigonometric polynomial fit wh...

This paper is concerned with a new approach to preconditioning for large sparse linear systems A procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient type methods Some theoretical properties of the preconditioner are discussed a...

A physically motivated near zone preconditioner is presented for solving the equations obtained from finite element method. Different from common sparse approximate inverse (SPAI) preconditioner, the proposed one gives the sparsity pattern based on a physical approximation. And its sparseness can be adjusted in different applications. The process of the algorithm needs low memory and CPU time, ...

The Bramble-Pasciak Conjugate Gradient method is a well known tool to solve linear systems in saddle point form. A drawback of this method in order to ensure applicability of Conjugate Gradients is the need for scaling the preconditioner which typically involves the solution of an eigenvalue problem. Here, we introduce a modified preconditioner and inner product which without scaling enable the...

Recently, in (M. Masoudi, D.K. Salkuyeh, An extension of positive-definite and skew-Hermitian splitting method for preconditioning generalized saddle point problems, Computers \& Mathematics with Application, https://doi.org/10.1016/j.camwa.2019.10.030, 2019) an the positive definite (EPSS) iteration nonsingular problems has been presented. In this article, we study semi-convergence EPSS singul...