Skip to main content
SpringerLink
Log in
Book cover

Numerical Validation in Current Hardware Architectures pp 103–116Cite as

Extending the Range of C-XSC: Some Tools and Applications for the Use in Parallel and Other Environments

  • Conference paper

  • 367 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5492))

Abstract

We present some examples of extensions for C-XSC that have been developed lately. Among these are extensions that give access to further hardware and software environments as well as application software using the new possibilities.

The first area of extension is C-XSC usage in parallel environments. An MPI package for C-XSC data types allows to easily use C-XSC in parallel software without bothering about the internal structure of data types. Different versions of parallel verified linear system solvers based on the package are now available. An application making use of these solvers and further extensions is a parallel verified Fredholm integral equation system solver. Some results are given to demonstrate the reduction of computation time and the accuracy gain that can be obtained.

Another possibility to extend the range of C-XSC is to export results to different software environments as, for example, computer algebra packages. An example of this is presented for the Maple interval package intpakX.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C-XSC: C-XSC Download, http://www.math.uni-wuppertal.de/wrswt/xsc/cxsc_new.html

  2. Hofschuster, W., Krämer, W.: C-XSC 2.0 – a C++ class library for extended scientific computing. In: Alt, R., Frommer, A., Kearfott, B., Luther, W. (eds.) Numerical Software with Result Verification (Dagstuhl Seminar 2003). LNCS, vol. 2991, pp. 15–35. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  3. Hammer, R., Hocks, M., Kulisch, U., Ratz, D.: C++ Toolbox for Verified Computing: Basic Numerical Problems. Springer, Heidelberg (1995)

    MATH  Google Scholar 

  4. Blomquist, F., Hofschuster, W., Krämer, W.: Real and complex Taylor Arithmetic in C-XSC. Preprint BUW-WRSWT 2005/4, University of Wuppertal (2005), http://www.math.uni-wuppertal.de/wrswt/literatur/lit_wrswt.html

  5. Bräuer, M.C.: Berechnungsmethoden für Ableitungen und Steigungen und deren Realisierung in C-XSC. Master’s thesis, University of Karlsruhe (1999)

    Google Scholar 

  6. El-Owny, H.: Verified Solution of Parametric Interval Linear Systems. Ph.D thesis, University of Wuppertal (2007)

    Google Scholar 

  7. Blomquist, F., Hofschuster, W., Krämer, W.: Real and Complex Staggered (Interval) Arithmetics with Wide Exponent Range (in German). Preprint BUW-WRSWT 2008/1, University of Wuppertal (2008), http://www.math.uni-wuppertal.de/wrswt/literatur/lit_wrswt.html

  8. Message Passing Interface Forum: MPI: A message passing interface standard. Library specification, University of Tennessee (1993-1995)

    Google Scholar 

  9. ALiCEnext: Alicenext information, http://www.alicenext.uni-wuppertal.de

  10. Hölbig, C., Krämer, W.: Selfverifying solvers for dense systems of linear equations realized in C-XSC. Preprint BUW-WRSWT 2003/1, University of Wuppertal (2003), http://www.math.uni-wuppertal.de/wrswt/literatur/lit_wrswt.html

  11. Rump, S.: Kleine Fehlerschranken bei Matrixproblemen. Ph.D thesis, University of Karlsruhe (1980)

    Google Scholar 

  12. Grimmer, M.: Selbstverifizierende mathematische Softwarewerkzeuge im High Performance Computing. Ph.D thesis, University of Wuppertal (2007)

    Google Scholar 

  13. Zimmer, M.: Laufzeiteffiziente, parallele Löser für lineare Intervallgleichungssysteme in C-XSC. Master’s thesis, University of Wuppertal (2007)

    Google Scholar 

  14. Ogita, T., Rump, S., Oishi, S.: Accurate sum and dot product. SIAM Journal on Scientific Computing 26(6), 1955–1988 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Heuser, H.: Funktionalanalysis. Teubner, Stuttgart (1975)

    MATH  Google Scholar 

  16. Klein, W.: Zur Einschließung der Lösung von linearen und nichtlinearen Fredholmschen Integralgleichungssystemen zweiter Art. Ph.D thesis, University of Karlsruhe (1990)

    Google Scholar 

  17. Klein, W.: Enclosure methods for linear and nonlinear systems of Fredholm integral equations of the second kind. In: Adams, E., Kulisch, U. (eds.) Scientific computing with automatic result verification, Boston. Academic Press, London (1993)

    Google Scholar 

  18. Grimmer, M.: Interval Arithmetic in Maple with intpakX. PAMM - Proceedings in Applied Mathematics and Mechanics 2(1), 442–443 (2003)

    Article  MATH  Google Scholar 

  19. Kress, R.: Linear Integral Equations. Springer, Heidelberg (1989)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CETEQ GmbH & Co. KG, 42119, Wuppertal, Lise-Meitner-Str. 5-9, Germany

    Markus Grimmer

Authors
  1. Markus Grimmer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, Universiteit Antwerpen, Middelheimlaan 1, 2020, Antwerpen, Belgium

    Annie Cuyt

  2. Wissenschaftliches Rechnen/Softwaretechnologie, Bergische Universität Wuppertal, Gausstrasse 20, 42097, Wuppertal, Germany

    Walter Krämer

  3. Fakultät Ingenieurwissenschaften, Abteilung Informatik und Angewandte Kognitionswissenschaft, Universität Duisburg-Essen, 47048, Duisburg, Germany

    Wolfram Luther

  4. 160 Redland Road, CA 94062, Woodside, USA

    Peter Markstein

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Grimmer, M. (2009). Extending the Range of C-XSC: Some Tools and Applications for the Use in Parallel and Other Environments. In: Cuyt, A., Krämer, W., Luther, W., Markstein, P. (eds) Numerical Validation in Current Hardware Architectures. Lecture Notes in Computer Science, vol 5492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01591-5_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-01591-5_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01590-8

  • Online ISBN: 978-3-642-01591-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation