Accelerated SOR-like method for augmented linear systems

By accelerating the SOR-like method by two parameters alpha and omega, we propose an accelerated SOR-like (ASOR) method for solving the augmented linear systems. The convergence of the ASOR method is discussed under suitable restrictions on the iteration parameters alpha and omega, and the experimental optimal values of the iteration parameters are determined. Numerical results are presented to show the efficiency of the ASOR method when the iteration parameters alpha and omega are suitably chosen.

[1]  Tie Zhang,et al.  A note on an SOR-like method for augmented systems , 2003 .

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

[3]  Howard C. Elman,et al.  Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics , 2014 .

[4]  Jinyun Yuan,et al.  Block SOR methods for rank-deficient least-squares problems , 1998 .

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

[6]  Howard C. Elman,et al.  Fast Nonsymmetric Iterations and Preconditioning for Navier-Stokes Equations , 1996, SIAM J. Sci. Comput..

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

[8]  Convergence for a general form of the GAOR method and its application to the MSOR method , 1994 .

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

[10]  A. Hadjidimos.  Successive overrelaxation (SOR) and related methods , 2000 .

[11]  Zhong-Zhi Bai,et al.  Optimal parameters in the HSS‐like methods for saddle‐point problems , 2009, Numer. Linear Algebra Appl..

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

[13]  Gene H. Golub,et al.  Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems , 2002, SIAM J. Matrix Anal. Appl..

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

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

[16]  Gene H. Golub,et al.  Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems , 2004, Numerische Mathematik.

[17]  Zeng-Qi Wang,et al.  On parameterized inexact Uzawa methods for generalized saddle point problems , 2008 .

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

[19]  Zhong-Zhi Bai,et al.  Structured preconditioners for nonsingular matrices of block two-by-two structures , 2005, Math. Comput..

[20]  Naimin Zhang,et al.  Optimal parameters of the generalized symmetric SOR method for augmented systems , 2014, J. Comput. Appl. Math..

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

[22]  Gene H. Golub,et al.  Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems , 2007 .

[23]  Jinyun Yuan,et al.  Numerical methods for generalized least squares problems , 1996 .

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

[25]  Changjun Li,et al.  A generalized successive overrelaxation method for least squares problems , 1998 .

[26]  Gene H. Golub,et al.  Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices , 2007, Math. Comput..

[27]  AN IMPROVED SYMMETRIC SOR ITERATIVE METHOD FOR AUGMENTED SYSTEMS , 2012 .

[28]  Zheng Li,et al.  Modified SOR-like method for the augmented system , 2007, Int. J. Comput. Math..