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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Convergence rates for Tikhonov regularization in finite-dimensional subspaces of Hilbert scales
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by Heinz W. Engl and Andreas Neubauer PDF
Proc. Amer. Math. Soc. 102 (1988), 587-592 Request permission

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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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 102 (1988), 587-592
  • MSC: Primary 65J10; Secondary 47A50
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0928985-X
  • MathSciNet review: 928985