IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-94-017-1247-7_2.html
   My bibliography  Save this book chapter

Influences of Rounding Errors in Solving Large Sparse Linear Systems

In: Developments in Reliable Computing

Author

Listed:
  • Axel Facius

    (Universität Karlsruhe (TH), Institut für Angewandte Mathematik)

Abstract

In many research areas like structural mechanics, economics, meteorology, and fluid dynamics, problems are mapped to large sparse linear systems via discretization. The resulting matrices are often ill-conditioned with condition numbers of about 1016 and higher. Usually these systems are preconditioned before they are fed to an iterative solver. Especially for ill-conditioned systems, we show that we have to be careful with these three classical steps — discretization, preconditioning, and (iterative) solving. For Krylov subspace solvers we give some detailed analysis and show possible improvements based on a multiple precision arithmetic. This special arithmetic can be easily implemented using the exact scalar product — a technique for computing scalar products of floating point vectors exactly.

Suggested Citation

  • Axel Facius, 1999. "Influences of Rounding Errors in Solving Large Sparse Linear Systems," Springer Books, in: Tibor Csendes (ed.), Developments in Reliable Computing, pages 17-30, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-1247-7_2
    DOI: 10.1007/978-94-017-1247-7_2
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-94-017-1247-7_2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.