Finite-dimensional approximation of constrained Tikhonov-regularized solutions of ill-posed linear operator equations

Author:
A. Neubauer

Journal:
Math. Comp. **48** (1987), 565-583

MSC:
Primary 65J10; Secondary 65R20

DOI:
https://doi.org/10.1090/S0025-5718-1987-0878691-2

MathSciNet review:
878691

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Abstract: In this paper we derive conditions under which the finite-dimensional constrained Tikhonov-regularized solutions of an ill-posed linear operator equation (i.e., is the minimizing element of the functional , in the closed convex set , which is a finite-dimensional approximation of a closed convex set *C*) converge to the best approximate solution of the equation in *C*. Moreover, we develop an estimate for the approximation error, which is optimal for certain sets *C* and . We present numerical results that verify the theoretical results.

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DOI:
https://doi.org/10.1090/S0025-5718-1987-0878691-2

Article copyright:
© Copyright 1987
American Mathematical Society