Electronic Resource
Springer
BIT
36 (1996), S. 287-301
ISSN:
1572-9125
Keywords:
Tikhonov regularization
;
regularization parameter
;
L-curve method
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This paper considers the Tikhonov regularization method with the regularization parameter chosen by the so-called L-curve criterion. An infinite dimensional example is constructed for which the selected regularization parameter vanishes too rapidly as the noise to signal ratio in the data goes to zero. As a consequence the computed reconstructions do not converge to the true solution. Numerical examples are given to show that similar phenomena can be observed under more general assumptions in “discrete ill-posed problems” provided the exact solution of the problem is “smooth”.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01731984
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