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.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.