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.
Reliable Computing – Springer Journals
Published: Oct 13, 2004
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