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Kernel-Splitting Technique for Enclosing the Solution of Fredholm Equations of the First Kind

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Reliable Computing

Abstract

We derive a numerical method for solving linear Fredholm integral equations of the first kind. Based on series expansion techniques, the kernel of the corresponding integral equation is splitted into a finite rank degenerate part and an infinite dimensional, normwise small remainder. By enclosing the remainder term, the original problem, is transformed into a degenerate set-valued problem. For this problem, we derive a numerical method that provides a rigorous control of approximation and roundoff errors. We show that this approach provides a regularization scheme.

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Authors and Affiliations

  1. Fb IMN, HTWK Leipzig, University of Applied Sciences, Box 300066, 04251, Leipzig, Germany

    Hans-Jürgen Dobner

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  1. Hans-Jürgen Dobner
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Dobner, HJ. Kernel-Splitting Technique for Enclosing the Solution of Fredholm Equations of the First Kind. Reliable Computing 8, 469–479 (2002). https://doi.org/10.1023/A:1021316610483

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  • DOI: https://doi.org/10.1023/A:1021316610483

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