Parallel solution of narrow banded diagonally dominant linear systems

Authors:
Carl Christian Kjelgaard Mikkelsen;Bo Kågström
Affiliations:
Department of Computing Science and HPC2N, Umeå University, Sweden;Department of Computing Science and HPC2N, Umeå University, Sweden
Venue:
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Year:
2010

Citing 5
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Abstract

ScaLAPACK contains a pair of routines for solving systems which are narrow banded and diagonally dominant by rows. Mathematically, the algorithm is block cyclic reduction. The ScaLAPACK implementation can be improved using incomplete, rather than complete block cyclic reduction. If the matrix is strictly dominant by rows, then the truncation error can be bounded directly in terms of the dominance factor and the size of the partitions. Our analysis includes new results applicable in our ongoing work of developing an efficient parallel solver.