Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Asymmetric Hermitian and skew-Hermitian splitting methods for positive definite linear systems
Computers & Mathematics with Applications
Restarted weighted full orthogonalization method for shifted linear systems
Computers & Mathematics with Applications
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We consider a three-dimensional convection-diffusion model problem and examine systems of equations arising from performing one step of cyclic reduction on an equally spaced mesh, discretized using the seven-point operator. We present two ordering strategies and analyze block splittings of the resulting matrices. If the matrices are consistently ordered relative to a given partitioning, Young's analysis for the block Gauss--Seidel and block SOR methods can be applied. We compare partitionings for which this property holds with ones where the matrices do not have Property A yet still give rise to an efficient solution process. Bounds on convergence rates are derived and the work involved in solving the systems is estimated.