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.
Titolo: | Solving inverse problems for delay integral equations using the "collage method" for fixed points |
Autori: | LA TORRE, DAVIDE (Secondo) |
Parole Chiave: | Fixed point equations ; Collage theorem ; Inverse problems |
Settore Scientifico Disciplinare: | Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie |
Data di pubblicazione: | 2012 |
Rivista: | |
Tipologia: | Article (author) |
Appare nelle tipologie: | 01 - Articolo su periodico |