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

Solving inverse problems for delay integral equations using the "collage method" for fixed points / H. Kunze, D. La Torre, K. Levere, E.R. Vrscay. - In: INTERNATIONAL JOURNAL OF MATHEMATICS AND STATISTICS. - ISSN 0974-7117. - 11:1(2012), pp. 1-11.

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

#### 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
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Fixed point equations ; Collage theorem ; Inverse problems
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/179139
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