Skip to main content
SpringerLink
Log in

Design of a parallel linear algebra library for verified computation

Разработка параллельной линейно-алгебраической библиотеки для верифицируемых вычислений

  • Mathematical Research
  • Published:
Reliable Computing

Abstract

In this paper we discuss design principles to implement a set of linear algebra subroutines in a portable libraty for parallel computers. Our design supports reuse of code and easy adaption to new parallel programming paradigms or network configurations.

The routines are supposed to be used in self-verifying algorithms. They therefore have to deliver a validated result of high accuracy.

Abstract

Обсуждаются принципы построения и реализации набора линейно-алгебраических подпрограмм переносимой библиотеки для параллельных компьютеров. Поддерживается повторное использование кода. Подпрограммы могуг легко адаптироваться к новым парадигмам параллельного программирования и сетевым конфигураниям.

Подпрограммы предназначены для использования в самоверифицирующих алгоритмах, позтому они дают достоверные результаты высокой точности.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bohlender, G. and Wolff von Gudenberg, J.Accurate matrix multiplication on the array processor AMT-DAP. In: Kaucher, Markov, and Mayer (eds) “Computer Arithmetic, Scientific Computation and Mathematical Modelling”, IMACS Annals on Computing and Applied Mathematics 12, Baltzer, Basel, 1992.

    Google Scholar 

  2. Choi, J., Dongarra, J., and Walker, D.LAPACK working note 57: PUMMA: parallel universal matrix multiplication algorithms on distributed memory concurrent computers. University of Tenessee, TR CS-93-187, 1993.

  3. Dongarra, J., Pozo, R., and Walker, D.LAPACK working note 61: an object oriented design for high performance linear algebra on distributed memory architectures. University of Tenessee, TR CS-93-200, 1993.

  4. Jézéquel, J. M., Bergheul, F., and André, F.Programming massively parallel arcitectures with sequential object oriented languages. FGCS10 (1) (1994), pp. 59–70.

    Google Scholar 

  5. Klatte, R., Kulisch, U., Neaga, M., Ratz, D., and Ullrich, Ch.PASCAL-XSC-language reference with examples. Springer, Berlin, 1992.

    Google Scholar 

  6. Klatte, R., Kulisch, U., Lawo, C., Rauch, M. and Wiethoff, A.C-XSC, a C++ class library for extended scientific computing. Springer, Berlin, 1993.

    Google Scholar 

  7. Reith, R.Wissenschaftliches Rechnen auf Multicomputern—BLAS-Routinen und die Lösung linearer Gleichungssysteme mit Fehlerkontrolle. Dissertation, Universität Basel, 1993.

  8. Wolff von Gudenberg, J.Modelling SIMD-type parallel arithmetic operations in Ada. In: Christodoulakis, D. (ed.) “Ada: The Choice for ’92”, LNCS 499, Springer, Berlin, 1991.

    Google Scholar 

  9. Wolff von Gudenberg, J.Accurate matrix operations on hypercube computers. In: Herzberger, J. and Atanassova, L. (eds) “Computer Arithmetic and Enclosure Methods”, North-Holland, Amsterdam, 1992.

    Google Scholar 

  10. Wolff von Gudenberg, J.Parallel accurate linear algebra subroutines. Reliable Computing1 (2) (1995), pp. 189–199.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lehrstuhl für Informatik II, Universität Würzburg, Am Hubland, D-97074, Würzburg, Germany

    J. Wolff von Gudenberg

Authors
  1. J. Wolff von Gudenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

von Gudenberg, J.W. Design of a parallel linear algebra library for verified computation. Reliable Comput 1, 411–419 (1995). https://doi.org/10.1007/BF02391686

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02391686

Keywords

Search

Navigation