Parallel Multisplitting Methods for Singular Linear Systems

Authors: Guangbin Wang, Fuping Tan

Abstract:

In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example.

Keywords: Singular H-matrix, linear systems, extrapolated iterative method, GMAOR method, convergence.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1060972

References:

[1] A. Hadjidimos and A. Yesios, The principle of extrapolation in connection with the accelerated overrelaxion method, Linear Algebra Appl., vol.30, pp.115-128, 1980.
[2] D. Wang, On the convergence of parallel multisplitting AOR algorithm, Linear Algebra Appl., vol.154-156, pp.473-486, 1991.
[3] A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York,1979.
[4] A. Neumaier, On the Comparison of H-matrices with M-matrices, Linear Algebra Appl., vol.83, pp.135-141, 1986.
[5] A. Frommer and D. B. Szyld, H-splittings and two-stage iterative methods, Numer Math., vol.63, pp.345-356, 1992.
[6] Y. Z. Song and L. Wang, On the semiconvergence of extrapolated iterative methods for singular linear systems, Appl. Numer. Math., vol.44, pp.401- 413, 2003.
[7] C. L. Wang and L. C. Zhang, Parallel Multisplitting Algorithms for Singular H-matrices, Numerical Mathematics(a Journal of Chinese Universities)( in Chinese), vol.1, pp.10-15, 2000.