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Solving inverse problems for deterministic and random delay integral equations using the “collage method”

H. E. Kunze, D. La Torre, K. M. Levere, E. R. Vrscay


We develop a collage coding framework for inverse problems involving delay integral equations. As with many other inverse problems, such a problem can be formulated in terms of approximating a target element u in a complete metric space (X; d) by the fixed point bar-x of a contractive operator. The collage coding method bounds the true error in this approximation by a more readily minimizable quantity. We extend the formulation to consider the associaed random integral equations with delay. We present several examples to illustrate the results.


fixed point equations, collage theorem, inverse problems, integral equations with delay

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