On the Parallel Technologies of Conjugate and Semi-conjugate Gradient Methods for Solving Very Large Sparse SLAEs

  • Valery P. Ilin
  • Dasha V. Knysh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4671)


The parallel technologies of iterative solving the symmetric and nonsymmetric systems of linear algebraic equations (SLAEs) with very large sparse matrices by means of conjugate and semi-conjugate gradient iterative methods are described. The performance computing for various matrix formats (diagonal, compressed sparse row/column), at the different degrees of freedom of SLAEs, are analysed. The results of experimental measurements under OPENMP, MPI and hybrid systems are presented and discussed.


Krylov Subspace Conjugate Gradient Algorithm Incomplete Factorization Parallel Technology Domain Decomposition Technique 
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  1. 1.
    Il’in, V.P.: Iterative Incomplete Factorization Methods. World Sci. Pub. Co., Singapore (1992)zbMATHGoogle Scholar
  2. 2.
    Saad, Y.: Iterative methods for sparse linear systems. PWS Publishing, New York (1996)zbMATHGoogle Scholar
  3. 3.
    Dongarra, J.J., Duff, I.S., Sorensen, D.C., Van der Vorst, H.A.: Solving Linear Systems on Vector and Shared Memory Computers. SIAM, Philadelphia (1991)Google Scholar
  4. 4.
    Juan, J.Y., Golub, G.H., Plemmons, R.J., Cecilio, A.B.: Semi-conjugate direction methods for real positive definite systems.–Techn. Rep. SCCM Pc 02-02, Stenford Univ. (2003)Google Scholar
  5. 5.
    Andreeva, M.Y., Il’in, V.P., Itskovich, E.A.: Two solvers for nonsymmetric SLAE Bulletin of the Novosibirs Computing Center. Num. Anal. 12(12), 1–16 (2004)Google Scholar
  6. 6.
    Il’in, V.P.: On the strategies of parallelization in mathematical modeling. Programming N 1, 41–46 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Valery P. Ilin
    • 1
    • 2
  • Dasha V. Knysh
    • 1
    • 2
  1. 1.Head of Laboratory, Institute of Computational, Mathematics and Mathematical Geophysics, SBRAS, Novosibirsk, Lavrentiev ave.,6, (383) 330-60-62 
  2. 2.PhD student, Novosibirsk State University, Novosibirsk, Pirogova str, 2, 8-913-754-56-15 

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