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Zeitschrift für Analysis und ihre Anwendungen


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Volume 14, Issue 2, 1995, pp. 369–377
DOI: 10.4171/ZAA/679

Published online: 1995-06-30

A Convergence Rate Result for a Steepest Descent Method and a Minimal Error Method for the Solution of Nonlinear Ill-Posed Problems

A. Neubauer[1] and Otmar Scherzer[2]

(1) Johannes Kepler Universität Linz, Austria
(2) Austrian Academy of Sciences, Linz, Austria

Recently, convergence and stability of the steepest descent method for the solution of nonlinear ill-posed operator equations have been proven. The same results also hold for the minimal error method. Since for ill-posed problems the convergence of iterative methods may be arbitrarily slow, it is of practical interest to guarantee convergence rates of the iterates under reasonable assumptions. The main emphasis of this paper is to present a convergence rate result in a uniform manner for the steepest descent and the minimal error method for the noise free case.

Keywords: Nonlinear ill-posed problems, steepest descent method, minimal error method, regularization methods, discrepancy principle, stopping rule

Neubauer A., Scherzer Otmar: A Convergence Rate Result for a Steepest Descent Method and a Minimal Error Method for the Solution of Nonlinear Ill-Posed Problems. Z. Anal. Anwend. 14 (1995), 369-377. doi: 10.4171/ZAA/679