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A class of discrepancy principles for the simplified regularization of ill-posed problems

Published online by Cambridge University Press:  17 February 2009

Santhosh George  and
M. Thamban Nair
M. Thamban Nair
Affiliation:
Department of Mathematics, Goa University, Goa — 403 203, India
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Abstract

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A class of discrepancy principles for the choice of parameters for the simplified regularization of ill-posed problems is proposed. This procedure does not require knowledge of the unknown solution, and if the smoothness of the unknown solution is known then the convergence rate obtained is optimal. The results of this paper include the Arcangeli's method considered by Groetsch and Guacaneme (1987) for which the convergence rate was not known and also of a result of Guacaneme (1988) for which there is a gap in the proof.

Type
Research Article
Information
The ANZIAM Journal , Volume 36 , Issue 2 , October 1994 , pp. 242 - 248
Copyright
Copyright © Australian Mathematical Society 1994

References

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