PSPIKE: A Parallel Hybrid Sparse Linear System Solver
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Performance models for the Spike banded linear system solver
Scientific Programming
A threaded SPIKE algorithm for solving general banded systems
Parallel Computing
Parallel solution of narrow banded diagonally dominant linear systems
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Incomplete cyclic reduction of banded and strictly diagonally dominant linear systems
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
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The truncated SPIKE algorithm is a parallel solver for linear systems which are banded and strictly diagonally dominant by rows. There are machines for which the current implementation of the algorithm is faster and scales better than the corresponding solver in ScaLAPACK (PDDBTRF/PDDBTRS). In this paper we prove that the SPIKE matrix is strictly diagonally dominant by rows with a degree no less than the original matrix. We establish tight upper bounds on the decay rate of the spikes as well as the truncation error. We analyze the error of the method and present the results of some numerical experiments which show that the accuracy of the truncated SPIKE algorithm is comparable to LAPACK and ScaLAPACK.