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FAST ONE-PARAMETER RELAXATION METHOD WITH A SCALED PRECONDITIONER FOR SADDLE POINT PROBLEMS
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 Title & Authors
FAST ONE-PARAMETER RELAXATION METHOD WITH A SCALED PRECONDITIONER FOR SADDLE POINT PROBLEMS
OH, SEYOUNG; YUN, JAE HEON;
 
 Abstract
In this paper, we first propose a fast one-parameter relaxation (FOPR) method with a scaled preconditioner for solving the saddle point problems, and then we present a formula for finding its optimal parameter. To evaluate the effectiveness of the proposed FOPR method with a scaled preconditioner, numerical experiments are provided by comparing its performance with the existing one or two parameter relaxation methods with optimal parameters such as the SOR-like, the GSOR and the GSSOR methods.
 Keywords
Relaxation iterative method;Saddle point problem;Preconditioner;Spectral radius;
 Language
English
 Cited by
 References
1.
M. Arioli, I.S. Duff, P.P.M. de Rijk, On the augmented system approach to sparse least squares problems, Numer. Math. 55 (1989), 667-684. crossref(new window)

2.
Z.Z. Bai, G.H. Golub, J.Y. Pan, Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems, Numer. Math. 98 (2004), 1-32. crossref(new window)

3.
Z.Z. Bai, B.N. Parlett, Z.Q. Wang, On generalized successive overrelaxation methods for augmented linear systems, Numer. Math. 102 (2005), 1-38. crossref(new window)

4.
Z. Chao, N. Zhang, Y.Z. Lu, Optimal parameters of the generalized symmetric SOR method for augmented systems, J. Comput. Appl. Math. 266 (2014), 52-60. crossref(new window)

5.
H. Elman, D.J. Silvester, Fast nonsymmetric iteration and preconditioning for Navier-Stokes equations, SIAM J. Sci. Comput. 17 (1996), 33-46. crossref(new window)

6.
B. Fischer, A. Ramage, D.J. Silvester, A.J. Wathen, Minimum residual methods for augmented systems, BIT 38 (1998), 527-543. crossref(new window)

7.
G.H. Golub, X. Wu, J.Y. Yuan, SOR-like methods for augmented systems, BIT 41 (2001), 71-85. crossref(new window)

8.
G.H. Santos, B.P.B. Silva, J.Y. Yuan, Block SOR methods for rank deficient least squares problems, J. Comput. Appl. Math. 100 (1998), 1-9. crossref(new window)

9.
S. Wright, Stability of augmented system factorization in interior point methods, SIAM J. Matrix Anal. Appl. 18 (1997), 191-222. crossref(new window)

10.
S.L. Wu, T.Z. Huang, X.L. Zhao, A modified SSOR iterative method for augmented systems, J. Comput. Appl. Math. 228 (2009), 424-433. crossref(new window)

11.
D.M. Young, Iterative solution of large linear systems, Academic Press, New York, 1971.

12.
J.Y. Yuan, A.N. Iusem, Preconditioned conjugate gradient methods for generalized least squares problem, J. Comput. Appl. Math. 71 (1996), 287-297. crossref(new window)

13.
SeYoung Oh, J.H. Yun, K.S. Kim, ESOR method with diagonal preconditioners for SPD linear systems, J. Appl. Math. & Informatics 33 (2015), 111-118. crossref(new window)

14.
G.F. Zhang, Q.H. Lu, On generalized symmetric SOR method for augmented systems, J. Comput. Appl. Math. 219 (2008), 51-58. crossref(new window)