The effective choice of the smoothing norm in regularization

Author:
Jane Cullum

Journal:
Math. Comp. **33** (1979), 149-170

MSC:
Primary 65R20; Secondary 41A25, 65D25

DOI:
https://doi.org/10.1090/S0025-5718-1979-0514816-1

MathSciNet review:
514816

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Abstract: We consider ill-posed problems of the form

*g*and

*K*are given, and we must compute

*f*. The Tikhonov regularization procedure replaces (1) by a one-parameter family of minimization problems-Minimize -where is a smoothing norm chosen by the user. We demonstrate by example that the choice of is not simply a matter of convenience. We then show how this choice affects the convergence rate, and the condition of the problems generated by the regularization. An appropriate choice for depends upon the character of the compactness of

*K*and upon the smoothness of the desired solution.

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DOI:
https://doi.org/10.1090/S0025-5718-1979-0514816-1

Article copyright:
© Copyright 1979
American Mathematical Society