Parallelism of double divide and conquer algorithm for singular value decomposition

  • Authors:

  • Taro Konda;Hiroaki Tsuboi;Masami Takata;Masashi Iwasaki;Yoshimasa Nakamura

  • Affiliations:

  • Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Sakyo-ku, Kyoto, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Sakyo-ku, Kyoto, Japan;Graduate School of Humanity and Science, Nara Women's University;SORST, JST;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Sakyo-ku, Kyoto, Japan and SORST, JST

  • Venue:
  • PDCN'07 Proceedings of the 25th conference on Proceedings of the 25th IASTED International Multi-Conference: parallel and distributed computing and networks
  • Year:
  • 2007

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Abstract

This paper presents some numerical evaluations of parallel double Divide and Conquer for singular value decomposition. For eigenvalue decomposition and singular value decomposition, double Divide and Conquer was recently proposed. It first computes eigen/singular values by a compact version of Divide and Conquer. The corresponding eigen/singular vectors are then computed 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. In addition, it is expected that double Divide and Conquer has great parallelism because each step is theoretically parallel and heavy communication is not required. This paper numerically evaluates a parallel implementation of dDC with MPI on some large scale problems using a distributed memory architecture and a massively parallel super computer, especially in terms of parallelism. It shows high scalability and super linear speed-up is observed in some cases.