Numerical approximation of minimum norm solutions of for special

Author:
Glenn R. Luecke

Journal:
Math. Comp. **53** (1989), 563-569

MSC:
Primary 65R20; Secondary 47A50, 65J10

DOI:
https://doi.org/10.1090/S0025-5718-1989-0983562-9

MathSciNet review:
983562

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Abstract: Let be continuous and linear and assume . Define by . Assume *K* has the property that (a) for all and (b) if -a.e., then for all . For example, if , is Lebesgue measure and if satisfies a Lipschitz condition in *x*, then *K* has the above property. Assume *K* satisfies this property and is a minimum norm solution of the first-kind integral equation for all . It is shown that is the -norm limit of linear combinations of the 's. It is then shown how to choose constants to minimize *without knowing what* *is*. This paper also contains results on how to choose the 's as well as numerical examples illustrating the theory.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1989-0983562-9

Keywords:
First-kind integral equation,
numerical solution of first-kind integral equations

Article copyright:
© Copyright 1989
American Mathematical Society