Solving inverse problems for delay and Hammerstein integral equations using the collage method for fixed points
Davide La Torre, University of Milan
Herb Kunze
Edward Vrscay
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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.
SUGGESTED CITATION:
Davide La Torre, Herb Kunze, and Edward Vrscay,
"Solving inverse problems for delay and Hammerstein integral equations using the collage method for fixed points"
(June 2006).
UNIMI - Research Papers in Economics, Business, and Statistics.
Statistics and Mathematics.
Working Paper 13.
http://services.bepress.com/unimi/statistics/art13
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