New methods for the localization of discontinuities of the first kind for functions of bounded variation / Ageev Alexandr L.,Antonova Tatyana V. // JOURNAL OF INVERSE AND ILL-POSED PROBLEMS. - 2013. - V. 21, l. 2. - P. 177-191.

ISSN/EISSN:

0928-0219 / нет данных

Type:

Article

Abstract:

We construct and study methods for approximating the positions (localization) of discontinuities of the first kind of a one-dimensional function. Instead of the exact function, its approximation in L-2(-infinity, +infinity and the perturbation level are known; smoothness conditions are imposed on the function outside the discontinuities. The number of discontinuities is countable, and all the discontinuities are divided into two sets: with the absolute value of the jump greater than some positive Delta(min) and discontinuities satisfying a smallness condition for the value of the jump. It is required to find the number of discontinuities in the first set and localize them using the approximately given function and the perturbation level. Since the problem is ill-posed, regularization algorithms should be used for its solution. Under additional conditions on the exact function, we construct regular methods for the localization of discontinuities and obtain estimates for the accuracy of localization and for the separability threshold, which is another important characteristic of the method. The order optimality of the constructed methods on classes of functions with discontinuities is established.

Author keywords:

Ill-posed problem; regularization algorithm; singularity localization; separability threshold

DOI:

10.1515/jip-2012-0039

Web of Science ID:

ISI:000317000300001

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	APR
Publisher	WALTER DE GRUYTER \& CO
Address	GENTHINER STRASSE 13, D-10785 BERLIN, GERMANY
Language	English
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	ageev@imm.uran.ru tvantonova@imm.uran.ru
Funding-Acknowledgement	Program for Fundamental Research of the Presidium of the Russian Academy of Sciences ``Dynamic Systems and Control Theory{''}; Ural Branch of the Russian Academy of Sciences {[}12-P-1-1022]; Russian Foundation for Basic Research {[}12-01-00106]
Funding-Text	This work was supported by the Program for Fundamental Research of the Presidium of the Russian Academy of Sciences ``Dynamic Systems and Control Theory{''
Number-of-Cited-References	23
Usage-Count-Since-2013	3
Journal-ISO	J. Inverse Ill-Posed Probl.
Doc-Delivery-Number	118CO