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On an algorithm for solving Fredholm integrals of the first kind

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Abstract

In this paper we use an iterative algorithm for solving Fredholm equations of the first kind. The basic algorithm and convergence properties are known under certain conditions, but we provide a simpler convergence proof without requiring the restrictive conditions that have previously been needed. Several examples of independent interest are given, including mixing density estimation and a first passage time density function involving Brownian motion. We also develop the basic algorithm to include functions which are not necessarily non-negative and, again, present illustrations.

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Acknowledgements

The authors are grateful for the reviewers’ helpful comments on a previous version of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, Cleveland, USA

    Minwoo Chae

  2. Department of Statistics, North Carolina State University, Raleigh, USA

    Ryan Martin

  3. Department of Mathematics, University of Texas at Austin, Austin, USA

    Stephen G. Walker

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  1. Minwoo Chae
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  2. Ryan Martin
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Correspondence to Minwoo Chae.

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Martin and Walker acknowledge NSF support with grants DMS-1611791 and DMS-1612891, respectively.

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Chae, M., Martin, R. & Walker, S.G. On an algorithm for solving Fredholm integrals of the first kind. Stat Comput 29, 645–654 (2019). https://doi.org/10.1007/s11222-018-9829-z

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