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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Asymptotic theory of filtering for linear operator equations with discrete noisy data
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by C. W. Groetsch and C. R. Vogel PDF
Math. Comp. 49 (1987), 499-506 Request permission

Abstract:

We consider Fredholm integral equations of the first kind with continuous kernels in which the data is discretely sampled and contaminated by white noise. A sufficient condition for the convergence of general filtering methods applied to such equations is derived. The condition in essence relates the decay rate of the singular values of the integral operator to the shape of the filter function used in the regularization method. Specific illustrations of the condition are given for Tikhonov regularization, the truncated singular value decomposition, and Landweber iteration.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 49 (1987), 499-506
  • MSC: Primary 65J10; Secondary 49D15, 65R20
  • DOI: https://doi.org/10.1090/S0025-5718-1987-0906184-2
  • MathSciNet review: 906184