The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Research Article

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

R. S. Anderssena1 and P. M. Prentera2

a1 Division of Mathematics and Statistics, C.S.I.R.O., P.O. Box 1965, Canberra City, A.C.T. 2601

a2 Colorado State University, Department of Mathematics, Fort Collins, Colorado 80523, U.S.A.

Abstract

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.

(Received August 07 1980)

(Revised November 26 1980)