Khimich, O. M.; Popov, O. V.; Chistyakov, O. V.; Sidoruk, V. A. 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. Cited in 1 Document MSC: 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 65Y05 Parallel numerical computation 15A18 Eigenvalues, singular values, and eigenvectors Keywords:algebraic eigenvalue problem; hybrid algorithm; subspace iterative method; efficiency of parallel algorithm; small-tiled algorithm Software:MKL; CUSPARSE PDFBibTeX XMLCite \textit{O. M. Khimich} et al., Cybern. Syst. Anal. 56, No. 6, 913--923 (2020; Zbl 1458.65038); translation from Kibern. Sist. Anal. 2020, No. 6, 61--74 (2020) 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/. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.