Some Results on Parallel Alternating Two-stage Methods
In this paper, we present parallel alternating two-stage
methods for solving linear system Ax=b, where A is a symmetric
positive definite matrix. And we give some convergence results of
these methods for nonsingular linear system.
[1] H. Migall├│n, V. Migall├│n, J. Penadés, "Alternating two-stage methods for
consistent linear system with applications to the parallel solution of
Markov chains," Advances in Engineering Software, vol.41,
pp.13-21,2010.
[2] B.L. Zhang, T.X. Gu, Z.Y. Mo, "Principles and methods of numerical
parallel computation," National defense industry Press, Beijing, 1999.
[3] W. Rheinboldt, J. Vandergraft, "A simple approach to the
Perron-Frobenius theory for positive operators on general
partially-ordered nite-dimensional linear spaces," Mathematics of
Computation, 27 (121) (1973) pp. 139-145.
[4] J.M. Ortega, Numerical Analysis, A second course, Academic Press, New
York, NY, 1972. Reprinted by SIAM, Philadelphia, PA, 1992.
[5] Castel MJ, Migall├│n V, Penadés J. "Convergence of non-stationary
parallel multisplitting methods for Hermitian positive denite matrices,"
Math Comput 1998;67(221): pp. 209-20.
[6] Migall├│n V, Penadés J. "Convergence of two-stage iterative methods for
Hermitian positive denite matrices," Appl Math Lett 1997;10(3): pp.
79-83.
[1] H. Migall├│n, V. Migall├│n, J. Penadés, "Alternating two-stage methods for
consistent linear system with applications to the parallel solution of
Markov chains," Advances in Engineering Software, vol.41,
pp.13-21,2010.
[2] B.L. Zhang, T.X. Gu, Z.Y. Mo, "Principles and methods of numerical
parallel computation," National defense industry Press, Beijing, 1999.
[3] W. Rheinboldt, J. Vandergraft, "A simple approach to the
Perron-Frobenius theory for positive operators on general
partially-ordered nite-dimensional linear spaces," Mathematics of
Computation, 27 (121) (1973) pp. 139-145.
[4] J.M. Ortega, Numerical Analysis, A second course, Academic Press, New
York, NY, 1972. Reprinted by SIAM, Philadelphia, PA, 1992.
[5] Castel MJ, Migall├│n V, Penadés J. "Convergence of non-stationary
parallel multisplitting methods for Hermitian positive denite matrices,"
Math Comput 1998;67(221): pp. 209-20.
[6] Migall├│n V, Penadés J. "Convergence of two-stage iterative methods for
Hermitian positive denite matrices," Appl Math Lett 1997;10(3): pp.
79-83.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:58233", author = "Guangbin Wang and Xue Li", title = "Some Results on Parallel Alternating Two-stage Methods", abstract = "In this paper, we present parallel alternating two-stage
methods for solving linear system Ax=b, where A is a symmetric
positive definite matrix. And we give some convergence results of
these methods for nonsingular linear system.", keywords = "alternating two-stage, convergence, linear system,parallel.", volume = "5", number = "8", pages = "1325-4", }