IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v457y2023ics0096300323003399.html
   My bibliography  Save this article

Note on a rank-one modification of the singular value decomposition

Author

Listed:
  • Baglama, James
  • Perović, Vasilije
  • Toolan, Timothy

Abstract

In this paper, we investigate the singular value decomposition (SVD) of Σ+xyH, where Σ is an m×n real diagonal matrix, x∈Cm, and y∈Cn. We start by briefly revisiting an existing approach for determining the desired SVD by sequentially computing the eigendecomposition of two separate hermitian rank-one modifications of a real diagonal matrix. Then we introduce the notion of the rank-two secular functionwhose roots are the singular values of Σ+xyH and exploit its properties to bound each root/singular value in disjoint intervals. Once the singular values are computed, we demonstrate how to directly compute the full set of associated left/right singular vectors ultimately giving us a new method for computing the SVD of Σ+xyH in O(min(m,n)2) time.

Suggested Citation

  • Baglama, James & Perović, Vasilije & Toolan, Timothy, 2023. "Note on a rank-one modification of the singular value decomposition," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    • Handle: RePEc:eee:apmaco:v:457:y:2023:i:c:s0096300323003399
    DOI: 10.1016/j.amc.2023.128170
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323003399
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2023.128170?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.

    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:apmaco:v:457:y:2023:i:c:s0096300323003399. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.