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

Author

Listed:
  • Davide La Torre

    (University of Milan)

  • Herb Kunze
  • Edward Vrscay

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 & Edward Vrscay, 2006. "Solving inverse problems for delay and Hammerstein integral equations using the collage method for fixed points," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1029, Universitá degli Studi di Milano.
    • Handle: RePEc:bep:unimip:unimi-1029
    Note: oai:cdlib1:unimi-1029
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