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The saturation phenomena for Tikhonov regularization

  • C. W. Groetsch (a1) and J. T. King (a1)

Abstract

This paper is concerned with a characterization of the optimal order of convergence of Tikhonov regularization for first kind operator equations in terms of the “smoothness” of the data.

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[1]Baker, C. T. H., The numerical tratment of integral equations, (Clarendon Press, Oxford, 1977).
[2]DeVore, R. A., The approximation of continuous functions by positive linear operators, (Lecture Notes in Mathematics Vol. 293, Springer-Verlag, Berlin, 1972).
[3]Groetsch, C. W., Generalized inverses of linear operators: representation and approximation, (Dekker, New York, 1977).
[4]Groetsch, C. W., ‘On a class of regularization methodsBoll. Un. Mat. Ital. (5) 17 (1980), 14111419.
[5]Groetsch, C. W., On the convergence of the method of regularization for equations of the first kind, (Numerical Analysis Report No. 52, 08, University of Manchester).
[6]Groetsch, C. W. and King, J. T., ‘Extrapolation and the method of regularization for generalized inverses’, J. Approximation Theory 25 (1979), 233247.
[7]Hilgers, J. W., Noniterative methods for solving operator equations of the first kind (Tech. Summ. Rep. 1413, Mathematics Research Center, Univ. of Wisconsin-Madison, 1973).
[8]Ivanov, V. V., The theory of approximate methods and their application to the numerical solution of singular integral equations, (Noordhoff, Leyden, 1976).
[9]King, J. T. and Chillingworth, D., ‘Approximation of generalized inverses by interated regularization’, Numer. Func. Anal. Optim. 1 (1979), 499513.
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