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Keldysh Institute preprints, 2017, 037, 28 pp. (Mi ipmp2253)  

This article is cited in 4 scientific papers (total in 4 papers)

Incomplete inverse triangular factorization in parallel algorithms of preconditioned conjugate gradient methods

I. E. Kaporin, O. Yu. Milyukova


Abstract: A preconditioner for large sparse symmetric positive definite coefficient matrix is considered based on its approximate inverse in the form of product of a lower triangular sparse matrix by its transpose. A parallel algorithm for the construction and application of the preconditioner is proposed. A new approximate block Jacobi preconditioning method is proposed based on the use of the incomplete inverse triangular factorization of diagonal blocks. Timing results are presented for a model problem and test problems with matrices from the collection of the university of Florida for the proposed preconditioning in comparison with the 2$^{\mathrm{nd}}$ order Block Incomplene Inverse Cholesky and the standard point Jacobi preconditionings.

Keywords: iterative solution of linear systems, sparse matrices, incomplete inverse triangular factorization, parallel preconditioning, conjugate gradient method.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00973_а
17-07-00510_а


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Citation: I. E. Kaporin, O. Yu. Milyukova, “Incomplete inverse triangular factorization in parallel algorithms of preconditioned conjugate gradient methods”, Keldysh Institute preprints, 2017, 037, 28 pp.

Citation in format AMSBIB
\Bibitem{KapMil17}
\by I.~E.~Kaporin, O.~Yu.~Milyukova
\paper Incomplete inverse triangular factorization in parallel algorithms of preconditioned conjugate gradient methods
\jour Keldysh Institute preprints
\yr 2017
\papernumber 037
\totalpages 28
\mathnet{http://mi.mathnet.ru/ipmp2253}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. E. Kaporin, O. Yu. Milyukova, “MPI+OpenMP parallelnaya realizatsiya metoda sopryazhennykh gradientov s nekotorymi yavnymi predobuslovlivatelyami”, Preprinty IPM im. M. V. Keldysha, 2018, 008, 28 pp.  mathnet  crossref  elib
    2. I. E. Kaporin, O. Yu. Milyukova, “MPI+OpenMPI realizatsiya metoda BiCGStab c faktorizovannym yavnym predobuslovlivatelem”, Preprinty IPM im. M. V. Keldysha, 2019, 047, 17 pp.  mathnet  crossref  elib
    3. O. Yu. Milyukova, “MPI+OpenMPI realizatsiya metoda sopryazhennykh gradientov s faktorizovannym predobuslovlivatelem”, Preprinty IPM im. M. V. Keldysha, 2020, 031, 22 pp.  mathnet  crossref
    4. O. Yu. Milyukova, “MPI+OpenMP realizatsiya metoda sopryazhennykh gradientov s predobuslovlivatelem blochnogo Yakobi IC1”, Preprinty IPM im. M. V. Keldysha, 2020, 083, 28 pp.  mathnet  crossref
  • Препринты Института прикладной математики им. М. В. Келдыша РАН
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