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 uR((A)p), 0<p12. In this note we slightly improve the rate for p=12 and also prove the rate O(δ13) if p>12.

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Key words

Lavrentiev regularization, convergence rates

AMS subject classifications

47A52, 65J20