On parameterized matrix splitting preconditioner for the saddle point problems. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Zheng, Q. Q.; Lu, L. Z.
• Is Part Of: International journal of computer mathematics. Volume 96:Issue 1(2019)
• Page Start: 1
• Page End: 17
• Publication Date: 2019-01-02
• Subjects: Saddle point problems -- matrix splittings -- iteration methods -- convergence analysis -- preconditioner; 65F10 -- 15A24; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2017.1420179
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: In this paper, we present a parameterized matrix splitting (PMS) preconditioner for the large sparse saddle point problems. The preconditioner is based on a parameterized splitting of the saddle point matrix, resulting in a fixed-point iteration. The convergence theorem of the new iteration method for solving large sparse saddle point problems is proposed by giving the restrictions imposed on the parameter. Based on the idea of the parameterized splitting, we further propose a modified PMS preconditioner. Some useful properties of the preconditioned matrix are established. Numerical implementations show that the resulting preconditioner leads to fast convergence when it is used to precondition Krylov subspace iteration methods such as generalized minimal residual method.