A NOTE ON OPTIMAL RATES FOR LAVRENTIEV REGULARIZATION WITH ADJOINT SOURCE CONDITIONS

In a recent paper, Plato, Mathe, 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 A u = f satisfies the adjoint source condition u is an element of R ((A*)(p)), 0 < p <= 1/2. In this note we slightly improve the rate for p = 1/2 and also prove the rate O (delta(1/3)) if p > 1/2.