On the localization of discontinuities of the first kind for a function of bounded variation / Ageev A. L.,Antonova T. V. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2013. - V. 280, l. 1. - P. 13-25.

ISSN/EISSN:

0081-5438 / нет данных

Type:

Article

Abstract:

Methods of the localization (detection of positions) of discontinuities of the first kind for a univariate function of bounded variation are constructed and investigated. Instead of an exact function, its approximation in L (2)(-a,+a) and the error level are known. We divide the discontinuities into two sets, one of which contains discontinuities with the absolute value of the jump greater than some positive Delta(min); the other set contains discontinuities satisfying a smallness condition for the value of the jump. It is required to find the number of discontinuities in the former set and localize them using the approximately given function and the error level. Since the problem is ill-posed, regularizing 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 the classes of functions with singularities is established.

Author keywords:

ill-posed problem; discontinuity of the first kind; localization of singularities; regularizing algorithm

DOI:

10.1134/S0081543813020028

Web of Science ID:

ISI:000317236500002

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	APR
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	ageev@imm.uran.ru tvantonova@imm.uran.ru
Funding-Acknowledgement	Ural Branch of the Russian Academy of Sciences {[}12-P-1-1022]; Russian Foundation for Basic Research {[}09-01-00053]
Funding-Text	This work was supported by the Ural Branch of the Russian Academy of Sciences (project no. 12-P-1-1022) within the Program for Fundamental Research of the Presidium of the Russian Academy of Sciences ``Dynamic Systems and Control Theory{''} and by the Russian Foundation for Basic Research (project no. 09-01-00053).
Number-of-Cited-References	19
Usage-Count-Since-2013	2
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	121IL