A modified SSOR iterative method for augmented systems. (English) Zbl 1167.65016
The authors propose the modified symmetric successive overrelaxation (MSSOR) method for solving the so called augmented systems. Such systems appear in many different applications of scientific computing: finite element approximation to solve Navier-Stokes equation, generalized least squares problems, constrained optimization, etc. The idea of the work is based on a result of M. T. Darvishi and P. Hessari, ”Symmetric Sor method for augmented systems”, Appl. Math. Comput. 183, No. 1, 409-415 (2006; Zbl 1111.65029)] on the solving of augmented systems by the symmetric successive overrelaxation (SOR) method.
To determine the optimal iteration parameter of the method and the corresponding optimal convergence factor, the authors propose a different splitting of the coefficient matrix of the system. A convergence analysis is also given. The conclusion of the authors is that the SOR-like method is superior to the MSSOR method for solving augmented systems. Two numerical examples are performed to illustrate how the MSSOR method works and to compare the MSSOR method to SOR-like method.
To determine the optimal iteration parameter of the method and the corresponding optimal convergence factor, the authors propose a different splitting of the coefficient matrix of the system. A convergence analysis is also given. The conclusion of the authors is that the SOR-like method is superior to the MSSOR method for solving augmented systems. Two numerical examples are performed to illustrate how the MSSOR method works and to compare the MSSOR method to SOR-like method.
Reviewer: Iulian Coroian (Baia Mare)
MSC:
| 65F10 | Iterative numerical methods for linear systems |
Keywords:
SOR like method; augmented systems; modified symmetric successive overrelaxation method; numerical examplesCitations:
Zbl 1111.65029References:
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