Solving an inverse problem for Urison-type integral equations using Banach s fixed point theorem
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Bibliographic record
Abstract
The solution of an Urison-type integral equation is the fixed point of an associated integral operator. The direct problem involves determining this fixed point when the operator is specified. We consider instead the following inverse problem: determine such an operator, in a restricted class, with fixed point close to a given target function, which may be an approximation or an interpolation of data points. We establish that these operators are contractive on an appropriate complete metric space and use Banach's fixed point theorem and related results, including the collage theorem, to develop a method of solution for the inverse problem. The technique involves the minimization of the distance between the target solution and its image under the integral operator, called the 'collage distance'. We discuss some ways to further reduce this distance.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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