An improvement of H. Wang preconditioner for L-matrices

Authors

  • Hamideh Nasabzadeh Bojnord University ,Iran

DOI:

https://doi.org/10.14419/ijamr.v5i4.5371

Published:

2016-10-21

Keywords:

Linear system, AOR method, Jacobi method, Gauss-Seidel method, Spectral radius, M-matrix, L-matrix, Preconditioner

Abstract

In this paper, we improve the preconditioner, that introduced by H. Wang et al [6]. The H. Wang preconditioner \(P\in R^{n\times n}\) has only one non-zero, non-diagonal element in \(P_{n1}\) or \(P_{1n}\) , when \(a_{1n}a_{n1}\ne 0\) . But the new preconditioner has only one non-zero, non-diagonal element in  \(P_{ij}\) or  \(P_{ji}\) if \(a_{ij}a_{ji}\ne 0\), so the H. Wang preconditioner is a spacial case of the new preconditioner for L-matrices. Also we present two models to construct a better \(I+S\) type preconditioner for the   \(AOR\) iterative method. Convergence analysis are given, numerical results are presented which show the effectiveness of the new preconditioners.

References

[1] A. Berman, R. J. Plemmons, Nonnegative Matrices in Mathematical Sciences,Academic Press, New York, 1979, SIAM,Philadelphia, PA, 1994.

[2] D.J. Evans, M.M. Martins, M.E. Trigo, The AOR iterative method for new preconditioned linear systems, Comput. Appl. Math. 132 (2001)461-466..

[3] A. Hadjidimos, Accelerated overrelaxation method, Math. Comp.32(1978) 149--157.

[4] Y. Li, C. Li, S. Wu, Improvements of preconditioned AOR iterative methods for L-matrices, J. Comput. Appl. Math. 206 (2007)656--665.

[5] R. S. Varga., Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, New York, 1962.

[6] H. Wang, Y. -t. Li,A new preconditioned AOR iterative method for L-matrices, J. Comput. Appl. Math. 229 (2009)47--53.

[7] L. Wang, Y. Song, Preconditioned AOR iterative methods for M-matrices, Comput. Appl. Math, 226(2009) 114--124.

[8] D. M. Young, Iterative Solution of Larg Linear Systems, Academic Press. New York, London, 1971.

[9] J. H. Yun, A note on preconditioned AOR method for L-matrices, J. Comput. Appl. Math. 220(2008) 13--16.

[10] Y. Zhang, T. -Z. Hung, Modified Iterative Methods for Nonnegative Matrices and M-matrices Linear systems, Comput. Math. Appl. 50(2005) 1587--1602.

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