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A parallel algorithm for solving a partial eigenvalue problem for block-diagonal bordered matrices. (English. Russian original) Zbl 1458.65038

Cybern. Syst. Anal. 56, No. 6, 913-923 (2020); translation from Kibern. Sist. Anal. 2020, No. 6, 61-74 (2020).
Summary: A hybrid algorithm of the iterative method for the solution subspace of a partial generalized eigenvalue problem for symmetric positive definite sparse matrices of block-diagonal structure with bordering on hybrid computers with graphic processors is proposed, efficiency coefficients of the algorithm are obtained, and the algorithm is tested against test and practical problems.

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65Y05 Parallel numerical computation
15A18 Eigenvalues, singular values, and eigenvectors

Software:

MKL; CUSPARSE
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Pissanetzky, S., Sparse Matrix Technology [Russian translation] (1988), Moscow: Mir, Moscow · Zbl 0536.65019
[2] Patlett, BN, The Symmetric Eigenvalue Problem [Russian translation] (1983), Moscow: Mir, Moscow · Zbl 0524.65023
[3] Boreskov, AV; Kharlamov, AA, Basics of CUDA Technology [in Russian] (2010), Moscow: Press, Moscow
[4] NetLib (2015). URL: http://www.netlib.org/.
[5] cuBLAS. URL: https://developer.nvidia.com/cublas.
[6] cuSparse Library. URL: http://docs.nvidia.com/cuda/cuSPARSE/.
[7] MAGMA. URL: http://icl.cs.utk.edu/magma/.
[8] AMD. URL: http://www.amd.com/en-gb.
[9] Intel® Math Kernel Library. URL: https://software.intel.com./en-us/mkl.
[10] SLEPc (2015). URL: http://slepc.upv.es/.
[11] LIS (2015). URL: http://www.ssisc.org/lis/.
[12] Khimich, AN; Molchanov, IN; Popov, AV; Chistyakova, TV; Yakovlev, MF, Parallel Algorithms to Solve Problems in Calculus Mathematics [in Russian] (2008), Kyiv: Naukova Dumka, Kyiv
[13] Khimich, OM; Sidoruk, VA, Hybrid algorithm for solving linear systems with sparse matrices based on the block LL^T method, Komp. Matematika, 1, 67-74 (2015)
[14] Khimich, AN; Popov, AV; Chistyakov, OV, Hybrid algorithms for solving the algebraic eigenvalue problem with sparse matrices, Cybern. Syst. Analysis, 53, 6, 937-949 (2017) · Zbl 1383.65030 · doi:10.1007/s10559-017-9996-5
[15] O. M. Khimich and V. A. Sydoruk, “Finely-tiled hybrid algorithm for the factorization of sparse matrix,” in: Informatics and Systems Sciences (ISS 2016): Proc. of the All-Ukrainian Scientific-Practical Conference with International Participation (Poltava, Ukraine, 19-21 March, 2016), PUET, Poltava (2016), pp. 326-328.
[16] Velikoivanenko, EA; Milenin, AS; Popov, AV; Sidoruk, VA; Khimich, AN, Methods and technologies of parallel computing for mathematical modeling of stress-strain state of constructions taking into account ductile fracture, J. Autom. Inform. Sci., 46, 11, 23-35 (2014) · doi:10.1615/JAutomatInfScien.v46.i11.30
[17] Sergienko, IV; Deineka, VS, Solving combined inverse problems for multicomponent parabolic distributed systems, Cybern. Syst. Analysis, 43, 5, 655-674 (2007) · Zbl 1153.35085 · doi:10.1007/s10559-007-0092-0
[18] Velikoivanenko, EA; Milenin, AS; Popov, AV; Sidoruk, VA; Khimich, AN, Methods of numerical forecasting of serviceability of welded structures on computers of hybrid architecture, Cybern. Syst. Analysis, 53, 1, 117-127 (2019) · doi:10.1007/s10559-019-00117-8
[19] Baranov, AY; Popov, AV; Slobodyan, YE; Khimich, AN, Mathematical modeling of building constructions using hybrid computing systems, J. Autom. Inform. Sci., 49, 7, 18-32 (2017) · doi:10.1615/JAutomatInfScien.v49.i7.20
[20] Popov, OV, Computer investigation of reliability of solutions to the generalized algebraic eigenvalue problem, Komp. Matematika, 1, 52-59 (2012)
[21] The SuiteSparse Matrix Collection. URL: https://cise.ufl.edu/research/sparse/matrices/.
[22] SCIT Supercomputer of V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine. URL: http://icybcluster.org.ua.
[23] Khimich, AN; Dekret, VA; Popov, AV; Chistyakov, AV, Numerical study of the stability of composite materials on computers of hybrid architecture, J. Autom. Inform. Sci., 50, 7, 7-24 (2018) · doi:10.1615/JAutomatInfScien.v50.i7.20
[24] Bystrov, VM; Dekret, VA; Zelenskii, VS, Numerical study of stability of layered composite material compressed by surface load, Problems of Computational Mechanics and Strength of Structures, 28, 23-33 (2018)
[25] MATLAB for deep learning. URL: https://mathworks.com/.
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