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The finite-section approximation for integral equations on the half-line

Published online by Cambridge University Press:  17 February 2009

Frank de Hoog  and
Ian H. Sloan
Frank de Hoog
Affiliation:
DMS, C.S.I.R.O., P.O. Box 1965, Canberra, A.C.T. 2601, Australia
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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Integral equations on the half line are commonly approximated by the finite-section approximation, in which the infinite upper limit is replaced by a positive number β. A novel technique is used here to rederive a number of classical results on the existence and uniqueness of the solution of the Wiener-Hopf and related equations, and is then extended to obtain existence, uniqueness and convergence results for the corresponding finite-section equations. Unlike the methods used in the recent work of Anselone and Sloan, the present methods are constructive, and result in explicit asymptotic bounds for the error introduced by the finite-section approximation.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 4 , April 1987 , pp. 415 - 434
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Anselone, P. M. and Sloan, I. H., “Integral equations on the half-line”, J. Integral Equations 9 (suppl.) (1985), 3–23.Google Scholar
[2]Atkinson, K. E., “The numerical solution of integral equations on the half-line,” SIAM J. Numer. Anal. 6 (1969), 375–397.CrossRefGoogle Scholar
[3]Jörgens, K., Linear integral operators (Pitman, Boston, 1982).Google Scholar
[4]Krasnosel'skii, M.A., “On a theorem of M. Riesz” Soviet Math. 1 (1960), 229–231.Google Scholar
[5]Krein, M.G., “Integral equatoins on a half-line with kernel depending on the difference of the arguments”, Amer. Math. Soc. Transl. (2) 22 (1963), 163–288.Google Scholar
[6]Sloan, I.H. and Spence, A., “Projection methods for integral equations on the half-line”, IMA J. Numer. Anal., (to appear)Google Scholar
[7]Wiener, N., The Fourier integral and certain of its applications (University Press, Cambridge, 1933).Google Scholar