Separate Reconstruction of Solution Components with Singularities of Various Types for Linear Operator Equations of the First Kind / Vasin V. V.,Soboleva E. O. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2015. - V. 289, l. 1. - P. S216-S226.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

Abstract:

A linear operator equation of the first kind is investigated. The solution of this equation contains singularities of various types; namely, along with a smooth background, the solution has sharp bends and jump discontinuities. For the construction of a stable approximated solution, a modified Tikhonov method with a stabilizer in the form of the sum of three functionals is proposed. Each of the functionals accounts for the specific character of the corresponding component of the solution. Convergence theorems are formulated, a general discrete approximation scheme of the regularizing algorithm is justified, and results of numerical experiments are discussed.

Author keywords:

Tikhonov method; ill-posed problem; solution with singularities; regularizing algorithm ILL-POSED PROBLEMS

DOI:

10.1134/S008154381505020X

Web of Science ID:

ISI:000356931500020

Соавторы в МНС:

—

Другие поля

Поле	Значение
Month	JUL
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
EISSN	1531-8605
Keywords-Plus	ILL-POSED PROBLEMS
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	vasin@imm.uran.ru soboleva@imm.uran.ru
Funding-Acknowledgement	Russian Foundation for Basic Research {[}12-01-00106]; Program for State Support of Leading Universities of the Russian Federation {[}02.A03.21.0006]
Funding-Text	This work was supported by the Russian Foundation for Basic Research (project no. 12-01-00106) and by the Program for State Support of Leading Universities of the Russian Federation (agreement no. 02.A03.21.0006 of August 27, 2013).
Number-of-Cited-References	20
Usage-Count-Since-2013	1
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	CL4OD