Volume 45, pp. 420-423, 2016.

A note on optimal rates for Lavrentiev regularization with adjoint source conditions

Andreas Neubauer

Abstract

In a recent paper, Plato, Mathé, and Hofmann proved several convergence rate results for Lavrentiev regularization. Especially, they also proved new results for the case when the exact solution $u$ of an ill-posed linear problem $Au=f$ satisfies the adjoint source condition $u\in\mathcal{R}({(A^*)^p})$, $0 < p\le\frac{1}{2}$. In this note we slightly improve the rate for $p=\frac{1}{2}$ and also prove the rate $O(\delta^\frac{1}{3})$ if $p > \frac{1}{2}$.

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Key words

Lavrentiev regularization, convergence rates

AMS subject classifications

47A52, 65J20

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