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Convergence rates for Tikhonov regularization in finite-dimensional subspaces of Hilbert scales


Authors: Heinz W. Engl and Andreas Neubauer
Journal: Proc. Amer. Math. Soc. 102 (1988), 587-592
MSC: Primary 65J10; Secondary 47A50
MathSciNet review: 928985
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Abstract: The main result of this paper states how the discretization parameter and regularization parameter should be chosen in relation to the noise level in order to yield the optimal convergence rate for the Tikhonov-regularized solution of an ill-posed linear operator equation in a finite-dimensional subspace in the framework of Hilbert scales. The results apply to a wide class of spline and finite-element subspaces of Sobolev scales.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0928985-X
Article copyright: © Copyright 1988 American Mathematical Society