Regularization of some linear ill-posed problems with discretized random noisy data

Mathé, Peter; Pereverzev, Sergei

doi:10.1090/S0025-5718-06-01873-4

Regularization of some linear ill-posed problems with discretized random noisy data
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by Peter Mathé and Sergei V. Pereverzev;

Math. Comp. 75 (2006), 1913-1929

DOI: https://doi.org/10.1090/S0025-5718-06-01873-4

Published electronically: June 28, 2006

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Abstract:

For linear statistical ill-posed problems in Hilbert spaces we introduce an adaptive procedure to recover the unknown solution from indirect discrete and noisy data. This procedure is shown to be order optimal for a large class of problems. Smoothness of the solution is measured in terms of general source conditions. The concept of operator monotone functions turns out to be an important tool for the analysis.

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