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An a Posteriori Parameter Choice for Tikhonov Regularization in Hilbert Scales Leading to Optimal Convergence Rates

Andreas Neubauer
SIAM Journal on Numerical Analysis
Vol. 25, No. 6 (Dec., 1988), pp. 1313-1326
Stable URL: http://www.jstor.org/stable/2157487
Page Count: 14
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An a Posteriori Parameter Choice for Tikhonov Regularization in Hilbert Scales Leading to Optimal Convergence Rates
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Abstract

An a posteriori parameter choice for Tikhonov regularization in Hilbert scales is proposed that leads to optimal convergence rates. The advantage of this method is that knowledge of the smoothness parameters of both the operator and the exact solution is not needed. The finite-dimensional realization of this method is also discussed. Numerical examples confirm the theoretical results.

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