IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v39y1995i1p21-37.html
   My bibliography  Save this article

Extending LINPACK by verification routines for linear systems

Author

Listed:
  • FalcóKorn, C.
  • Ullrich, C.P.

Abstract

LINPACK is a well known and heavily used software library which offers a collection of routines to solve linear algebra problems. A major drawback of LINAPACK and similar packages is the fact that the provided routines merely compute an approximation for the solution of a given problem. In some cases, a user can get an estimation of the achieved accuracy, but these estimations may give way to a misleading interpretation of the computed solution. Therefore, we show how to extend several LINPACK procedures by the capability of computing a guaranteed inclusion of the solution. For solving linear systems based on factorizations (e.g. LU or Cholesky method), this extension can be established without changing the given library, thus reusing the existing software. Furthermore, runtime and accuracy measurements show for H-matrices that the verification can be achieved with less costs than the computation of the estimation—especially for banded matrices of high dimension.

Suggested Citation

  • FalcóKorn, C. & Ullrich, C.P., 1995. "Extending LINPACK by verification routines for linear systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(1), pages 21-37.
    • Handle: RePEc:eee:matcom:v:39:y:1995:i:1:p:21-37
    DOI: 10.1016/0378-4754(94)00133-5
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378475494001335
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/0378-4754(94)00133-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    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:eee:matcom:v:39:y:1995:i:1:p:21-37. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.