Heterogeneous distribution of computations while solving linear algebra problems on networks of heterogeneous computers

  • Alexey Kolinov
  • Alexey Lastovetsky
Track C2: Computational Science
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1593)


The paper presents a heterogeneous distribution of computations while solving dense linear algebra problems on heterogeneous networks of computers. The distribution is based on heterogeneous block cyclic distribution which is extension of the traditional homogeneous block cyclic distribution taking into account differences in the processor performances. The mpC language, specially designed for parallel programming heterogeneous networks is briefly introduced. An mpC aplication carring out Cholesky factorization on a heterogenous network of workstations is used to demonstrate that the heterogeneous distribution have an essential advantage over the traditional homogeneous distribution.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. S. Blackford, A. Cleary, J. Demmel, I. Dhillon, J. Dongarra S. Hammarling, A. Petitet, H. Ren, K. Stanley, and R. C. Whaley Practical Experience in the Dangers of Heterogeneous Computing UT, CS-96-330, July 1996.Google Scholar
  2. 2.
    D. Arapov, A. Kalinov, A. Lastovetsky, I. Ledovskih, and T. Lewis “A Programming Environment for Heterogeneous Distributed Memory Machines”, Proceedings of the Sixth Heterogeneous Computing Workshop (HCW'97), IEEE Computer Society Press, Geneva, Switzerland, April 1, 1997.Google Scholar
  3. 3.
    A. Lastovetsky, The mpC Programming Language Specification. Technical Report, ISPRAS, Moscow, December 1994.Google Scholar
  4. 4.
    B. Hendrickson and D. Womble,” The Torus-wrap Mapping for Dense Matrix Calculations on Massively Parallel Computers”, SIAMSSC, 15(5), 1994.Google Scholar
  5. 5.
    J. Choi, J. J. Dongarra, S. Ostrouchov, A. P. Petitet, D. W. Walker, and R. C. Whaley “The Design and Implementation of the ScaLAPACK LU, QR, and Cholesky Factorization Routines” UT, CS-94-246, September, 1994.Google Scholar
  6. 6.
    D.Arapov, A. Kalinov, A. Lastovetsky and I. Ledovskih “Experiments with mpC: Efficient Solving Regular Problems on Heterogeneous Networks of Computers via Irregularization”, Proceedings of the Fifth International Symposium on Solving Irregularty Structure Problems in Parallel (IRREGULAR'98), Lecture Notes in Computer Science 1457, Berkley, CA, USA, August 9–11, 1998.Google Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • Alexey Kolinov
    • 1
  • Alexey Lastovetsky
    • 1
  1. 1.Institute for System ProgrammingRussian Academy of SciencesMoscowRussia

Personalised recommendations