On the modified symmetric successive over-relaxation method for augmented systems

Recently, Darvishi and Hessari (Comput Math Appl 61:3128–3135, 2011) introduced a modified SSOR method for augmented systems. In this paper, we establish an improvement SSOR method for solving the large sparse augmented systems, which is the extension of the modified SSOR method. The convergence analysis of our method is studied under suitable restrictions on iteration parameters. Furthermore, the functional equation between the parameters and the eigenvalues of the iteration matrix of this method is obtained. Finally, numerical computations are presented based on a particular linear system, which clearly show the effectiveness of our algorithm.

[1]  Ke Wang,et al.  SSOR-like methods for saddle point problems , 2009, Int. J. Comput. Math..

[2]  Beresford N. Parlett,et al.  On generalized successive overrelaxation methods for augmented linear systems , 2005, Numerische Mathematik.

[3]  David J. Evans,et al.  Chebyshev acceleration for SOR-like method , 2005, Int. J. Comput. Math..

[4]  G. Golub,et al.  Inexact and preconditioned Uzawa algorithms for saddle point problems , 1994 .

[5]  Gene H. Golub,et al.  A Preconditioner for Generalized Saddle Point Problems , 2004, SIAM J. Matrix Anal. Appl..

[6]  Eric de Sturler,et al.  Block-Diagonal and Constraint Preconditioners for Nonsymmetric Indefinite Linear Systems. Part I: Theory , 2005, SIAM J. Sci. Comput..

[7]  J. Pasciak,et al.  Iterative techniques for time dependent Stokes problems , 1997 .

[8]  Walter Zulehner,et al.  Analysis of iterative methods for saddle point problems: a unified approach , 2002, Math. Comput..

[9]  Guo-Feng Zhang,et al.  On generalized symmetric SOR method for augmented systems , 2008 .

[10]  M. T. Darvishi,et al.  A modified symmetric successive overrelaxation method for augmented systems , 2011, Comput. Math. Appl..

[11]  M. Madalena Martins,et al.  A variant of the AOR method for augmented systems , 2012, Math. Comput..

[12]  Richard S. Varga,et al.  Matrix Iterative Analysis , 2000, The Mathematical Gazette.

[13]  Ting-Zhu Huang,et al.  A modified SSOR iterative method for augmented systems , 2009 .

[14]  Ting-Zhu Huang,et al.  Convergence of a generalized MSSOR method for augmented systems , 2012, J. Comput. Appl. Math..

[15]  Å. Björck,et al.  Solution of augmented linear systems using orthogonal factorizations , 1994 .

[16]  Wen Li,et al.  On unsymmetric block overrelaxation-type methods for saddle point problems , 2008, Appl. Math. Comput..

[17]  E. Sturler,et al.  Block-diagonal and constraint preconditioners for nonsymmetric indefinite linear systems , 2006 .

[18]  Gene H. Golub,et al.  SOR-like Methods for Augmented Systems , 2001 .

[19]  M. T. Darvishi,et al.  Symmetric SOR method for augmented systems , 2006, Appl. Math. Comput..

[20]  A. Wathen,et al.  Minimum residual methods for augmented systems , 1998 .

[21]  Stephen J. Wright.  Stability of Augmented System Factorizations in Interior-Point Methods , 1997, SIAM J. Matrix Anal. Appl..

[22]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[23]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .