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

Davide La Torre, Herb Kunze and Edward Vrscay

No unimi-1029, UNIMI - Research Papers in Economics, Business, and Statistics from Universitá degli Studi di Milano

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.

Keywords: Fixed point equations; collage theorem; inverse problems (search for similar items in EconPapers)
Date: 2006-06-23
Note: oai:cdlib1:unimi-1029
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