A class of Uzawa-SOR methods for saddle point problems

• Published in: Applied mathematics and computation Vol. 216; no. 7; pp. 2163 - 2168
• Main Authors: Zhang, Jianjun, Shang, Jijuan
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.06.2010; Elsevier
• Subjects: 65F10; 65F50; Acceleration of convergence; Algebra; Algebraic geometry; Classification; Conjugate gradient methods; Convergence; Exact sciences and technology; Iterative methods; Linear systems; Mathematical analysis; Mathematical models; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Saddle point problems; Saddle points; Sciences and techniques of general use; SOR methods; Uzawa method; Workload; 65F50; Uzawa method; 65F10; Conjugate gradient methods; Iterative methods; SOR methods; Saddle point problems; Convergence; Conjugate gradient method; Convergence acceleration; Numerical linear algebra; Iterative method; Iteration; Direct method; Experimental result; Numerical analysis; Linear system; Linear equation; Matrix inversion; Applied mathematics; Overrelaxation method; Convergence rate
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2010.03.051

In this paper, we consider a class of Uzawa-SOR methods for saddle point problems, and prove the convergence of the proposed methods. We solve a lower triangular system per iteration in the proposed methods, instead of solving a linear equation Az = b . Actually, the new methods can be considered as an inexact iteration method with the Uzawa as the outer iteration and the SOR as the inner iteration. Although the proposed methods cannot achieve the same convergence rate as the GSOR methods proposed by Bai et al. [Z.-Z. Bai, B.N. Parlett, Z.-Q. Wang, On generalized successive overrelaxation methods for augmented linear systems, Numer. Math. 102 (2005) 1–38], but our proposed methods have less workloads per iteration step. Experimental results show that our proposed methods are feasible and effective.