Parallel Multisplitting Methods for Singular Linear Systems
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:54491", author = "Guangbin Wang and Fuping Tan", title = "Parallel Multisplitting Methods for Singular Linear Systems", 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.", volume = "4", number = "7", pages = "874-4", }