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An Optimal Stopping Rule for the v-Method for Solving Ill-Posed Problems, Using Christoffel Functions

✍ Scribed by M. Hanke; H.W. Engl


Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
639 KB
Volume
79
Category
Article
ISSN
0021-9045

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✦ Synopsis


We design an order-optimal stopping rule for the (\nu)-method for solving ill-posed problems with noisy data. The construction of the (\nu)-method is based on a sequence of Jacobi polynomials, and the stopping rule is based on a sequence of related Christoffel functions. The motivation for our stopping criterion arises from a careful comparison between the iterates of the (\nu)-method and the approximations obtained from iterated Tikhonov regularization with (noninteger) order (\nu). The convergence results rely on asymptotic properties of the Christoffel functions. 1994 Academic Press. Inc.