Restoration of a potential from noisy spectral dataстатья
Информация о цитировании статьи получена из
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Дата последнего поиска статьи во внешних источниках: 28 сентября 2017 г.
Авторы:
Ternovskii V.V. ,
Khapaeva T.M. ,
Khapaev M.M.
Журнал:
Doklady Mathematics
Том:
96
Номер:
1
Год издания:
2017
Издательство:
Maik Nauka/Interperiodica Publishing
Местоположение издательства:
Russian Federation
Первая страница:
403
Последняя страница:
405
DOI:
10.1134/S1064562417040251
Аннотация:
Interest in the inverse Sturm–Liouville problem is motivated by its numerous applications in mathematics and computational physics. To solve a complete inverse problem, one needs two exact spectra, which are usually not known in experimental spectroscopy. Accordingly, a problem of interest is to restore the potential from a finite set of noisy spectral data. A new variational method for solving inverse spectral problems is proposed, which is based on the regularization of ill-posed problems. The method takes into account the measurement error of the spectrum and restores the potential without using simplifying assumptions that it belongs to a certain functional class. The method has been tested on potentials involving smooth segments and jump discontinuities.
Original Russian Text © V.V. Ternovskii, T.M. Khapaeva, M.M. Khapaev, 2017, published in Doklady Akademii Nauk, 2017, Vol. 475, No. 5, pp. 508–510.
Presented by Academician of the RAS V.A. Sadovnichii March 15, 2017
Добавил в систему:
Терновский Владимир Владимирович