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Convergence of degenerate-kernel methods

Published online by Cambridge University Press:  17 February 2009

Ian H. Sloan
Ian H. Sloan
Affiliation:
Department of Applied Mathematics, University of New South Wales, Sydney, N.S.W. 2033, Australia.
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Abstract

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Additional convergence results are given for the approximate solution in the space L2(a, b) of Fredholm integral equations of the second kind, y = f + Ky, by the degenerate-kernel methods of Sloan, Burn and Datyner. Convergence to the exact solution is provided for a class of these methods (including ‘method 2’), under suitable conditions on the kernel K, and error bounds are obtained. In every case the convergence is faster than that of the best approximate solution of the form yn = Σnan1u1, where u1, …, un are the appropriate functions used in the rank-n degenerate-kernel approximation. In addition, the error for method 2 is shown to be relatively unaffected if the integral equation has an eigenvalue near 1.

Type
Research Article
Information
The ANZIAM Journal , Volume 19 , Issue 4 , December 1976 , pp. 422 - 431
Copyright
Copyright © Australian Mathematical Society 1976

References

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