IDEAS home Printed from https://ideas.repec.org/a/wly/navlog/v12y1965i1p119-132.html
   My bibliography  Save this article

Finding the inverse and connections of a type of large sparse matrix

Author

Listed:
  • Martin Hershkowitz
  • Stedman B. Noble

Abstract

Much interest is being shown in methods for determining structure of matrices in order to simplify computation. This paper takes a slightly different approach, giving an algorithm that determines the structure of a matrix while inverting it. The algorithm applies to matrices with dominant diagonal or similar matrices that can be inverted using the C. Neumann series. This series is decomposed into terms which are products of connected coefficients: the procedure lends itself to an efficient method of truncation that obtains an approximation to the inverse matrix. While this algorithm might not be efficient for some matrices, it is quite efficient for the 430‐order Minkowski‐Leontief matrix upon which it was tested. Furthermore, the computation enumerates the connections in the matrix; hence the model can be “tested” by comparing the connections of the model with those known to exist in the underlying phenomena.

Suggested Citation

  • Martin Hershkowitz & Stedman B. Noble, 1965. "Finding the inverse and connections of a type of large sparse matrix," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(1), pages 119-132, March.
    • Handle: RePEc:wly:navlog:v:12:y:1965:i:1:p:119-132
    DOI: 10.1002/nav.3800120107
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.3800120107
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.3800120107?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
    ---><---

    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:wly:navlog:v:12:y:1965:i:1:p:119-132. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1931-9193 .

    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.