naa a22 4500 510811833 CHVBK 20180411083446.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1134/S0081543813020028 doi (NATIONALLICENCE)springer-10.1134/S0081543813020028 On the localization of discontinuities of the first kind for a function of bounded variation [Elektronische Daten] [A. Ageev, T. Antonova] 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(−∞,+∞) 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 Δmin; 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. Pleiades Publishing, Ltd., 2013 ill-posed problem nationallicence discontinuity of the first kind nationallicence localization of singularities nationallicence regularizing algorithm nationallicence Ageev A. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, 620990, Yekaterinburg, Russia aut Antonova T. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, 620990, Yekaterinburg, Russia aut Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280(2013-04-01), 13-25 0081-5438 280<13 2013 280 11501 https://doi.org/10.1134/S0081543813020028 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813020028 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ageev A. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, 620990, Yekaterinburg, Russia aut NATIONALLICENCE 700 1- Antonova T. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, 620990, Yekaterinburg, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280(2013-04-01), 13-25 0081-5438 280<13 2013 280 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer