Use of parallel level 3 BLAS in LU factorization on three vector multiprocessors the ALLIANT FX/80, the CRAY-2, and the IBM 3090 VF

  • Authors:

  • M. J. Daydé;I. S. Duff

  • Affiliations:

  • CERFACS, 42 Av. G. Coriolis, 31047 Toulouse Cedex, France and ENSEEIHT-IRIT, 2 rue Camichel 31071 Toulouse Cedex, France;CERFACS, 42 Av. G. Coriolis, 31047 Toulouse Cedex, France and CSS Division, Harwell Laboratory, OXON OX11 0RA, England

  • Venue:
  • ICS '90 Proceedings of the 4th international conference on Supercomputing
  • Year:
  • 1990

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Abstract

We show how to transform the B-spline curve and surface fitting problems into suffix computations of continued fractions. Then a parallel substitution scheme is introduced to compute the suffix values on a newly proposed mesh-of-unshuffle network. The derived parallel algorithm allows the curve interpolation through n points to be solved in &Ogr;(log n) time using &THgr;n/log n) processors and allows the surface interpolation through m x n points to be solved in &Ogr;(log m log n) time using &THgr; (mn/(log m log n)) processors. Both interpolation algorithms are cost-optimal for their respective problems. Besides, the surface fitting problem can be even faster solved in &Ogr;(log m + log n) time if &THgr;(mn) processors are used in the network.