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A Communication Avoiding and Reducing Algorithm for Symmetric Eigenproblem for Very Small Matrices A Communication Avoiding and Reducing Algorithm for Symmetric Eigenproblem for Very Small Matrices Takahiro, Katagiri Jun'ichi, Iwata Kazuyuki, Uchida Takahiro, Katagiri Jun'ichi, Iwata Kazuyuki, Uchida 線形代数 In this paper, a parallel symmetric eigensolver with very small matrices in massively parallel processing is considered. We define very small matrices that fit the sizes of caches per node in a supercomputer. We assume that the sizes also fit the exa-scale computing requirements of current production runs of an application. To minimize communication time, we added several communication avoiding and communication reducing algorithms based on Message Passing Interface (MPI) non-blocking implementations. A performance evaluation with up to full nodes of the FX10 system indicates that (1) the MPI non-blocking implementation is 3x as efficient as the baseline implementation, (2) the hybrid MPI execution is 1.9x faster than the pure MPI execution, (3) our proposed solver is 2.3x and 22x faster than a ScaLAPACK routine with optimized blocking size and cyclic-cyclic distribution, respectively. In this paper, a parallel symmetric eigensolver with very small matrices in massively parallel processing is considered. We define very small matrices that fit the sizes of caches per node in a supercomputer. We assume that the sizes also fit the exa-scale computing requirements of current production runs of an application. To minimize communication time, we added several communication avoiding and communication reducing algorithms based on Message Passing Interface (MPI) non-blocking implementations. A performance evaluation with up to full nodes of the FX10 system indicates that (1) the MPI non-blocking implementation is 3x as efficient as the baseline implementation, (2) the hybrid MPI execution is 1.9x faster than the pure MPI execution, (3) our proposed solver is 2.3x and 22x faster than a ScaLAPACK routine with optimized blocking size and cyclic-cyclic distribution, respectively. 情報処理学会 2015-02-23 eng technical report https://ipsj.ixsq.nii.ac.jp/records/113232 AN10463942 研究報告ハイパフォーマンスコンピューティング（HPC） 2015-HPC-148 2 1 17 https://ipsj.ixsq.nii.ac.jp/record/113232/files/IPSJ-HPC15148002.pdf application/pdf 1.7 MB 2017-02-23