Abstract
In this paper we consider a dual gradient method for solving linear ill-posed problems Ax = y, where A : X rightarrow Y is a bounded linear operator from a Banach space X to a Hilbert space Y. A strongly convex penalty function is used in the method to select a solution with desired feature. Under variational source conditions on the sought solution, convergence rates are derived when the method is terminated by either an a priori stopping rule or the discrepancy principle. We also consider an acceleration of the method as well as its various applications.
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