Modified SSOR-like method for augmented systems

• Main Authors: Chun Wen, Ting-Zhu Huang
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2011-08-01
• Series: Mathematical Modelling and Analysis
• Subjects: SOR-like method; SSOR-like method; augmented system; saddle point problem; MSSOR-like method
• Online Access: https://journals.vgtu.lt/index.php/MMA/article/view/5554
• ISSN: 1392-6292; 1648-3510

For solving the augmented system, Golub, Wu and Yuan and Zheng, Wang and Wu have presented the SOR-like methods and SSOR-like methods, respectively. In this paper, the SSOR-like method with two real parameters ω and α is established for solving the augmented system, which is the extension of the SSOR iteration method, and the new method is called the modified SSOR-like method (MSSOR-like method). The convergence of the MSSOR-like method is studied, and the function equation relating the parameters and eigenvalues of the iteration matrix of this method is obtained. Numerical experiments show that the MSSOR-like method with proper preconditioning matrix and parameters is better than the SOR-like method and the SSOR-like method.