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Article

Šípek, Jan ; Zítko, Jan
Alternating iterative scheme for the solution of block-structured systems. (English). In: Chleboun, J., Přikryl, P. and Segeth, K. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 6-11, 2004. Institute of Mathematics AS CR, Prague, 2004. pp. 214-229
Summary:
We consider the solution of linear system with a block-structured matrix of saddle point type. The solution technique is based on the idea of the classical alternating-direction implicit iterative method where symmetric-antisymmetric splitting of the coefficient matrix is used. To find an optimal parameter for solving the system with a symmetric matrix, the polynomial filters are considered. The CGW method is used for systems with skew-symmetric matrix. The numerical tests compare the results obtained by using alternating iteration and GMRES and point out advantages of alternative iterations for larger systems.
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