A parallel algorithm for accurate dot product

Journal
Parallel computing  
Volume
34
Issue
6-8
Start Page
392
End Page
410
Citation
Parallel Computing 34 (6-8): 392-410 (2008)
Publisher DOI
10.1016/j.parco.2008.02.002
Scopus ID
2-s2.0-44349101763
Publisher
North-Holland, Elsevier Science
Parallel algorithms for accurate summation and dot product are proposed. They are parallelized versions of fast and accurate algorithms of calculating sum and dot product using error-free transformations which are recently proposed by Ogita et al. [T. Ogita, S.M. Rump, S. Oishi, Accurate sum and dot product, SIAM J. Sci. Comput. 26 (6) (2005) 1955-1988]. They have shown their algorithms are fast in terms of measured computing time. However, due to the strong data dependence in the process of their algorithms, it is difficult to parallelize them. Similarly to their algorithms, the proposed parallel algorithms in this paper are designed to achieve the results as if computed in K-fold working precision with keeping the fastness of their algorithms. Numerical results are presented showing the performance of the proposed parallel algorithm of calculating dot product.
Subjects
Accurate dot product
Accurate summation
Higher precision
Parallel algorithm
DDC Class
004: Informatik
510: Mathematik