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A formal comparison of methods proposed for the numerical solution of first kind integral equations

Published online by Cambridge University Press:  17 February 2009

R. S. Anderssen  and
P. M. Prenter
R. S. Anderssen
Affiliation:
Division of Mathematics and Statistics, C.S.I.R.O., P.O. Box 1965, Canberra City, A.C.T. 2601
P. M. Prenter
Affiliation:
Colorado State University, Department of Mathematics, Fort Collins, Colorado 80523, U.S.A.
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Abstract

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A formal framework is constructed for the comparison of different stabilization techniques, such as Wiener filtering, regularization, Courant's method and Landweber–Strand iterations, for the solution of first kind integral equations. It is shown that, when they are applied to convolution equations, all these methods can be reinterpreted as Wiener filters. This equivalence is then used to derive some specific results about regularization, Courant's method and Landweber–Strand iteration.

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 4 , April 1981 , pp. 488 - 500
Copyright
Copyright © Australian Mathematical Society 1981

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