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Uniform convergence of regularization methods for Fredholm equations of the first kind

Part of: Fredholm integral equations Theoretical approximation of solutions Numerical analysis: Ordinary differential equations

Published online by Cambridge University Press:  09 April 2009

C. W. Groetsch
C. W. Groetsch
Affiliation:
Department of Mathematical SciencesUniversity of CincinnatiCincinnati, Ohio 45221, U.S.A.
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Abstract

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For Fredholm equations of the first kind with continuous kernels we investigate the uniform convergence of a general class of regularization methods. Applications are made to Tikhonov regularization and Landweber's iteration method.

MSC classification

Secondary: 45L05: Theoretical approximation of solutions 45B05: Fredholm integral equations 65L05: Initial value problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 2 , October 1985 , pp. 282 - 286
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Groetsch, C. W., The theory of Tikhonov regularization for Fredholm equations of the first kind (Research Notes in Mathematics, vol. 105, Pitman Books Ltd., London, 1984).Google Scholar
[2]Groetsch, C. W., ‘On a class of regularization methods’, Boll. Un. Mat. Ital. B 5 (1980), 1411–1419.Google Scholar
[3]Khudak, Yu. I., ‘On the regularization of solutions of integral equations of the first kind’, USSR Comput. Math. and Math. Phys. 6 (No. 4) (1966), 217–221.CrossRefGoogle Scholar
[4]Landweber, L., ‘An iteration formula for Fredholm integral equations of the first kind’, Amer. J. Math. 73 (1951), 615–624.CrossRefGoogle Scholar
[5]Tikhonov, A. N. and Arsenin, V. Y., Solutions of ill-posed problems (Wiley, New York, 1977 (translated from the Russian)).Google Scholar