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Iterative parameter choice by discrepancy principle. (English) Zbl 1261.65052

The authors are concerned with the numerical implementation of the discrepancy principle for nonsmooth Tikhonov regularization for linear inverse problems. They discuss some theoretical properties of the solutions to the discrepancy equation, namely, uniqueness and upper bounds. By Padé approximation, they design model functions with model parameters iteratively updated. For the efficient numerical realization, they propose two algorithms. To demonstrate the accuracy of the principle and to illustrate the efficiency and robustness of the proposed algorithms, they present numerical experiments.

MSC:

65J10 Numerical solutions to equations with linear operators
65J22 Numerical solution to inverse problems in abstract spaces
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
47A52 Linear operators and ill-posed problems, regularization
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