Accelerated SOR-like method for augmented linear systems

Abstract

By accelerating the SOR-like method by two parameters alpha and omega, we propose an accelerated SOR-like (ASOR) method for solving the augmented linear systems. The convergence of the ASOR method is discussed under suitable restrictions on the iteration parameters alpha and omega, and the experimental optimal values of the iteration parameters are determined. Numerical results are presented to show the efficiency of the ASOR method when the iteration parameters alpha and omega are suitably chosen.

On the optimal convergence factor of the accelerated parameterized inexact Uzawa method with three parameters for augmented systems

“…If functions satisfy then becomes the method in the GSOR‐like family that is defined in the work of Huang and Zhou . Clearly, the methods that are defined in other works are special members of this family with the special choice of functions . Here, we only list functions for methods in other works, which are not included in the work of Huang and Zhou …”

“…Clearly, the methods that are defined in other works are special members of this family with the special choice of functions . Here, we only list functions for methods in other works, which are not included in the work of Huang and Zhou …”

“…If we choose and then becomes the accelerated SOR‐like method in the work of Njeru and Guo …”

“…then (68) becomes the method in the GSOR-like family that is defined in the work of Huang and Zhou. 17 Clearly, the methods that are defined in other works 12,[18][19][20][21][22][23][24] are special members of this family with the special choice of functions , g, h.…”

Editorial Preface: “Advances in numerical algebra and scientific computing”

“…There were 10 invited keynote speakers, 29 contributed talks, and 10 poster presentations. This issue of BIT Numerical Mathematics contains carefully selected and refereed papers by participants who delivered oral and poster presentations at the conference.The papers discuss the HSS iteration method and its generalizations for the solution of large sparse non-Hermitian positive definite systems of linear equations [8], iterative methods and preconditioning techniques based on matrix splittings for large sparse saddle-point problems [2,3,[5][6][7]9,11], the iterated Tikhonov regularization method for the solution of large-scale Tikhonov minimization problems [4], rigorous convergence analysis of alternating variable minimization with multiplier methods for quadratic programming problems with equality constraints [1], and modeling the interaction of flow and molecular orientation in a complex fluid of nematic liquid crystals [10].The topics covered at NASC 2014 include direct and iterative methods for systems of linear and nonlinear equations; preconditioning and Krylov subspace iter- …”