Parallel algorithms and condition estimators for standard and generalized triangular Sylvester-type matrix equations

Authors:
Robert Granat;Bo Kågström
Affiliations:
Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden;Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden
Venue:
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Year:
2006

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Abstract

We discuss parallel algorithms for solving eight common standard and generalized triangular Sylvester-type matrix equation. Our parallel algorithms are based on explicit blocking, 2D block-cyclic data distribution of the matrices and wavefront-like traversal of the right hand side matrices while solving small-sized matrix equations at different nodes and updating the rest of the right hand side using level 3 operations. We apply the triangular solvers in condition estimation, developing parallel sep-1-estimators. Some experimental results are presented.