IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v148y2011i1d10.1007_s10957-010-9739-5.html
   My bibliography  Save this article

Global Saturation of Regularization Methods for Inverse Ill-Posed Problems

Author

Listed:
  • Terry Herdman

    (Virginia Tech)

  • Ruben D. Spies

    (IMAL, CONICET-UNL
    Universidad Nacional del Litoral)

  • Karina G. Temperini

    (IMAL, CONICET-UNL
    Universidad Nacional del Litoral)

Abstract

In this article the concept of saturation of an arbitrary regularization method is formalized based upon the original idea of saturation for spectral regularization methods introduced by Neubauer (Beiträge zur angewandten Analysis und Informatik, pp. 262–270, 1994). Necessary and sufficient conditions for a regularization method to have global saturation are provided. It is shown that for a method to have global saturation the total error must be optimal in two senses, namely as optimal order of convergence over a certain set which at the same time, must be optimal (in a very precise sense) with respect to the error. Finally, two converse results are proved and the theory is applied to find sufficient conditions which ensure the existence of global saturation for spectral methods with classical qualification of finite positive order and for methods with maximal qualification. Finally, several examples of regularization methods possessing global saturation are shown.

Suggested Citation

  • Terry Herdman & Ruben D. Spies & Karina G. Temperini, 2011. "Global Saturation of Regularization Methods for Inverse Ill-Posed Problems," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 164-196, January.
    • Handle: RePEc:spr:joptap:v:148:y:2011:i:1:d:10.1007_s10957-010-9739-5
    DOI: 10.1007/s10957-010-9739-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-010-9739-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-010-9739-5?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.

    References listed on IDEAS

    as
    1. T. Herdman & R. D. Spies & K. G. Temperini, 2009. "Generalized Qualification and Qualification Levels for Spectral Regularization Methods," Journal of Optimization Theory and Applications, Springer, vol. 141(3), pages 547-567, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      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:joptap:v:148:y:2011:i:1:d:10.1007_s10957-010-9739-5. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.