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

Kernel-Splitting Technique for Enclosing the Solution of Fredholm Equations of the First Kind 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

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

, Volume 8 (6) – Oct 13, 2004
11 pages

/lp/springer_journal/kernel-splitting-technique-for-enclosing-the-solution-of-fredholm-7ZXln3wpS3
Publisher
Springer Journals
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1021316610483
Publisher site
See Article on Publisher Site

### 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.

### Journal

Reliable ComputingSpringer Journals

Published: Oct 13, 2004

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