ANALYSIS OF THE TRUNCATED SPIKE ALGORITHM

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MİKKELSEN C., MANGUOĞLU M.

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, cilt.30, sa.4, ss.1500-1519, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 30 Sayı: 4
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1137/080719571
  • Dergi Adı: SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1500-1519
  • Anahtar Kelimeler: direct methods, banded, and row diagonally dominant linear systems, BANDED SYSTEM SOLVER, PARALLEL
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

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.