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Basic techniques for numerical linear algebra on bulk synchronous parallel computers

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Numerical Analysis and Its Applications (WNAA 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1196))

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Abstract

The bulk synchronous parallel (BSP) model promises scalable and portable software for a wide range of applications. A BSP computer consists of several processors, each with private memory, and a communication network that delivers access to remote memory in uniform time.

Numerical linear algebra computations can benefit from the BSP model, both in terms of simplicity and efficiency. Dense LU decomposition and other computations can be made more efficient by using the new technique of two-phase randomised broadcasting, which is motivated by a cost analysis in the BSP model. For LU decomposition with partial pivoting, this technique reduces the communication time by a factor of (√p+1)/3, where p is the number of processors.

Theoretical analysis, together with benchmark values for machine parameters, can be used to predict execution time. Such predictions are verified by numerical experiments on a 64-processor Cray T3D. The experimental results confirm the advantage of two-phase randomised broadcasting.

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Authors and Affiliations

  1. Department of Mathematics, Utrecht University, P. O. Box 80010, 3508, TA Utrecht, the Netherlands

    Rob H. Bisseling

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  1. Rob H. Bisseling
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Lubin Vulkov Jerzy Waśniewski Plamen Yalamov

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© 1997 Springer-Verlag Berlin Heidelberg

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Bisseling, R.H. (1997). Basic techniques for numerical linear algebra on bulk synchronous parallel computers. In: Vulkov, L., Waśniewski, J., Yalamov, P. (eds) Numerical Analysis and Its Applications. WNAA 1996. Lecture Notes in Computer Science, vol 1196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62598-4_78

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  • DOI: https://doi.org/10.1007/3-540-62598-4_78

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62598-8

  • Online ISBN: 978-3-540-68326-1

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