ANALYSIS OF THE TRUNCATED SPIKE ALGORITHM


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MİKKELSEN C., MANGUOĞLU M.

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, vol.30, no.4, pp.1500-1519, 2008 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 4
  • Publication Date: 2008
  • Doi Number: 10.1137/080719571
  • Title of Journal : SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
  • Page Numbers: pp.1500-1519
  • Keywords: direct methods, banded, and row diagonally dominant linear systems, BANDED SYSTEM SOLVER, PARALLEL

Abstract

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.