Applied Convergence Results of Relaxed Matrix Multisplitting Chaotic Methods for H-Matrices

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Abstract:

In this paper, based on the methods presented Song, Yuan [Int. J. Comput. Math., 52 (1994) 195-20, we present relaxed matrix multisplitting chaotic generalized USAOR-style methods by introducing more relaxed parameters and analyze some applied convergence results of methods to be convenient for carrying out numerical experiments.

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February 2014

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[1] R. Bru, L. Elsner, M. Neumman, Models of parallel chaotic iterative methods, Linear Algebra Appl. 103(1988) 175-192.

DOI: 10.1016/0024-3795(88)90227-3

Google Scholar

[2] D. Chazan W. Miranker, Chaotic relaxation, Linear Algebra Appl. 2(1969) 199-222.

DOI: 10.1016/0024-3795(69)90028-7

Google Scholar

[3] L. Elsner, M. Neumman, B. Vemmer, The e?ect the number of processors on the convergence of the parallel block Jacobi method, Linear Algebra Appl. 154-156 (1991) 311-330.

DOI: 10.1016/0024-3795(91)90382-7

Google Scholar

[4] A. Frommer, G. Mayer, Convergence of relaxed parallel multisplitting methods, Linear Algebra Appl. 119 (1989) 141-152.

DOI: 10.1016/0024-3795(89)90074-8

Google Scholar

[5] T. X. Gu, X. P. Liu, L. J. Shen, Relaxed parallel two-stage multisplitting methods, Int. J. Comput. Math. 75 (2000) 351-363.

Google Scholar

[6] T. X. Gu, X. P. Liu, Parallel two-stage multisplitting iterative methods, Int. J. Comput. Math. 20(2)(1998) 153-166.

Google Scholar

[7] Mas J. et al., Nonstationary parallel relaxed multisplitting methods, Linear Algebra Appl. 241-243 (1992) 733-747.

DOI: 10.1016/0024-3795(95)00583-8

Google Scholar

[8] P. E. Kloeden, D. Yuan, Comvergence of relaxed chaotic parallel iterative methods, Bull. Aust. Math. Soc. 50 (1994) 167-176.

DOI: 10.1017/s0004972700009655

Google Scholar

[9] D. P. O'Leary, R. E. White, Multi-splittings of matrices and parallel solution of linear systems, SIAM Journal on Algebraic and Discrete Mathematics, 6 (1985) 630-640.

DOI: 10.1137/0606062

Google Scholar

[10] W. C. Rheinholdt, J. S. Vandergrafy, A simple approach to the Perron-Frobenius theory for positive perators on general partially-ordered finite-dimension linear spaces, Math. Comput. 27 (1973) 139-145.

DOI: 10.1090/s0025-5718-1973-0325650-4

Google Scholar

[11] Y. Song, On the convergence of the generalized AOR method, Linear Algebra Appl. 256 (1997) 199-218.

DOI: 10.1016/s0024-3795(96)00028-6

Google Scholar

[12] Y. Song, D. Yuan, Ontheconvergenceofrelaxedparallelchaoticiterationsfor H-matrix, Int. J. Comput. Math. 52 (1994) 195-209.

Google Scholar

[13] R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cli?s, NJ, (1962).

Google Scholar

[14] D. Yuan, OntheconvergenceofparallelmultisplittingasynchronousGAORmethod for H-matrix, Appl. Math. Comput. 160 (2005) 477-485.

Google Scholar

[15] Y. Zhang, The USAOR iterative method for linear systems (in Chinese), Numerical Mathematics, 9 (4) (1987) 354-365.

Google Scholar