# Solving inverse problems for delay and Hammerstein integral equations using the collage method for fixed points

## Author Info

• Davide La Torre

(University of Milan)

• Herb Kunze
• Edward Vrscay
Registered author(s):

## Abstract

Many inverse problems in applied mathematics can be formulated as the approximation of a target element $u$ in a complete metric space $(X,d)$ by the fixed point $\bar x$ of an appropriate contraction mapping $T : X \to X$. The method of {\em collage coding} seeks to solve this problem by finding a contraction mapping $T$ that minimizes the so-called {\em collage distance} $d(x,Tx)$. In this paper, we develop a collage coding framework for inverse problems involving two classes of integral equations -- those with delay and Hammerstein-type equations. We illustrate the method with some practical examples.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://services.bepress.com/unimi/statistics/art13

## Bibliographic Info

Paper provided by Universitá degli Studi di Milano in its series UNIMI - Research Papers in Economics, Business, and Statistics with number unimi-1029.

as
in new window

 Length: Date of creation: 23 Jun 2006 Date of revision: Handle: RePEc:bep:unimip:unimi-1029 Note: oai:cdlib1:unimi-1029 Contact details of provider: Postal: Via Conservatorio 7 - 20122 MilanoPhone: +39 02 503 16486Fax: +39 02 503 16475Web page: http://services.bepress.com/unimiMore information through EDIRC

## References

No references listed on IDEAS
You can help add them by filling out this form.

## Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

## Corrections

When requesting a correction, please mention this item's handle: RePEc:bep:unimip:unimi-1029. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.