Some Results on Parallel Alternating Methods

Authors: Guangbin Wang, Fuping Tan

Abstract:

In this paper, we investigate two parallel alternating methods for solving the system of linear equations Ax = b and give convergence theorems for the parallel alternating methods when the coefficient matrix is a nonsingular H-matrix. Furthermore, we give one example to show our results.

Keywords: Nonsingular H-matrix, parallel alternating method, convergence.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1057691

References:

[1] M.Benzi and D.B.Syzld, Existence and uniqueness of splttings for stationary iterative methods with applications to alternating methods, Numer. Math., vol.76, 309-321, 1997.
[2] J.-J.Climent, C.Perea, L.Tortosa and A.Zamora, Convergence theorems for parallel alternating iterative methods, Appl. Math. and Comp., vol.148, pp.497-517, 2004.
[3] L.Elsner, Comparisons of weak regular splittings and multisplitting methods, Numer.Math., vol.56, pp.283-289, 1989.
[4] R.S.Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1962.
[5] H. Schneider, Theorems on M-splittings of a singular M-matrix which depend on graph structure, Linear Algebra Appl., vol.58, pp.407-424, 1984.
[6] A.Frommer and D.B.Szyld, H-splittings and two-stage iterative methods, Numer Math., vol.63, pp.345-356, 1992.
[7] A. Ostrowski, Uber die determinant mit uberwiegenber hauptdiagonale, Comment Math. Heh., vol.10, pp.69-96, 1937.