Prefix algorithms for tridiagonal systems on hypercube multiprocessors

Authors:
O. Egecioglu;C. K. Koc;A. J. Laub
Affiliations:
Deparnnent of Computer Science, University of California, Santa Barbara, CA;Scientific Computation Laboratory, Department of Electrical & Computer Engineering, University of California, Santa Barbara, CA;Scientific Computation Laboratory, Department of Electrical & Computer Engineering, University of California, Santa Barbara, CA
Venue:
C3P Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2
Year:
1989

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C3P Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2

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Abstract

The recursive doubling algorithm as developed by Stone can be used to solve a tridiagonal linear system of size n on a parallel computer with n processors using &Ogr; ( log n ) parallel arithmetic steps. Here we describe a limited processor version of the recursive doubling algorithm for the solution of tridiagonal linear systems using &Ogr; ( n / p + log p ) parallel arithmetic steps on a parallel computer with p processors. The main technique relies on fast parallel prefix algorithms, which can be efficiently mapped on the hypercube architecture using the binary-reflected Gray code. For pn this algorithm achieves linear speed-up and constant efficiency over its sequential implementation as well as over the sequential LU decomposition algorithm. These results are confirmed by numerical experiments obtained on an Intel iPSC/d5 hypercube multiprocessor.