Parallel Double Divide and Conquer and its Evaluation on a Super Computer

T. Konda and Y. Nakamura (Japan)


Parallel Computing, Singular Value Decomposition, Nu merical Analysis, Eigenvalue Decomposition, Linear Al gebra


This paper presents comprehensive evaluations of parallel double Divide and Conquer for singular value decomposi tion on a super computer, HPC2500. For bidiagonal SVD, double Divide and Conquer was proposed. It first com putes singular values by a compact version of Divide and Conquer. The corresponding singular vectors are then com puted by twisted factorization. The speed and accuracy of double Divide and Conquer are as good or even better than standard algorithms such as QR and the original Divide and Conquer. Moreover, it shows high scalability even on a PC cluster, distributed memory architecture. Parallel algorithm of dDC and numerical results in some architectural options, matrix sizes and types on HPC2500, SMP cluster is shown.

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