Parallel Algorithms for Triangular Periodic Sylvester-Type Matrix Equations

Authors:
Per Andersson;Robert Granat;Isak Jonsson;Bo Kågström
Affiliations:
Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden SE-901 87;Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden SE-901 87;Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden SE-901 87;Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden SE-901 87
Venue:
Euro-Par '08 Proceedings of the 14th international Euro-Par conference on Parallel Processing
Year:
2008

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Abstract

We present parallel algorithms for triangular periodic Sylves-ter-type matrix equations, conceptually being the third step of a periodic Bartels---Stewart-like solution method for general periodic Sylvester-type matrix equations based on variants of the periodic Schur decomposition. The presented algorithms are designed and implemented in the framework of the recently developed HPC library SCASY and are based on explicit blocking, 2-dimensional block cyclic data distribution and a wavefront-like traversal of the right hand side matrices. High performance is obtained by rich usage of level 3 BLAS operations. It is also demonstrated how several important key concepts of SCASY regarding communications and the treatment of quasi-triangular coefficient matrices are generalized to the periodic case. Some experimental results from a distributed memory Linux cluster demonstrate are also presented.