IDEAS home Printed from https://ideas.repec.org/a/rsk/journ0/7954858.html
   My bibliography  Save this article

Adjoint differentiation for generic matrix functions

Author

Listed:
  • Andrei Goloubentsev
  • Dmitri Goloubentsev
  • Evgeny Lakshtanov

Abstract

We derive a formula for the adjoint Ā of a square-matrix operation of the form f(A), where f is holomorphic in the neighborhood of each eigenvalue.We consider special cases such as the spectral decomposition A = UDU-1 and the spectrum cutoff f(A) = A+ for symmetric A. We then apply the formula to derive closed-form expressions in particular cases of interest to quantitative finance such as the “nearest correlation matrix†routine and regularized linear regression.

Suggested Citation

  • Andrei Goloubentsev & Dmitri Goloubentsev & Evgeny Lakshtanov, . "Adjoint differentiation for generic matrix functions," Journal of Computational Finance, Journal of Computational Finance.
    • Handle: RePEc:rsk:journ0:7954858
    as

    Download full text from publisher

    File URL: https://www.risk.net/journal-of-computational-finance/7954858/adjoint-differentiation-for-generic-matrix-functions
    Download Restriction: no
    ---><---

    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:rsk:journ0:7954858. 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: Thomas Paine (email available below). General contact details of provider: https://www.risk.net/journal-of-computational-finance .

    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.