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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


IMPACT FACTOR increased in 2014: 0.880
Rank 74 out of 310 in category Mathematics and 113 out of 255 in Applied Mathematics in the 2014 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2014: 0.516
Source Normalized Impact per Paper (SNIP) 2014: 1.430
Impact per Publication (IPP) 2014: 0.613

Mathematical Citation Quotient (MCQ) 2014: 0.51

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Localization algorithms for singularities of solutions to convolution equations of the first kind

A. L. Ageev1 / T. V. Antonova2

1Institute of Mathematics and Mechanics UrB RAS, Kovalevskaya st., 16, 620219 Ekaterinburg, Russia. Email:

2Institute of Mathematics and Mechanics UrB RAS, Kovalevskaya st., 16, 620219 Ekaterinburg, Russia. Email:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 16, Issue 7, Pages 639–650, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2008.039, November 2008

Publication History

Received:
2008-02-02
Published Online:
2008-11-21

Abstract

In this paper we construct and investigate localization algorithms for isolated singularities of a function which is a solution to a linear convolution equation of the first kind whose right-hand side is given with an error. We consider two types of singularities: δ-functions and discontinuities of the first kind. A problem for singularities localization is an ill-posed problem having perturbation. We use averaging methods defined by an averaging functional to obtain the singularities. We formulate conditions that the averaging functional must satisfy. For convolution equations, using the Fourier transform, we obtained upper estimates of precision of the singularities localization, separation threshold and other important characteristics of the supposed methods.

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[3]
T. V. Antonova
Numerical Analysis and Applications, 2010, Volume 3, Number 4, Page 306
[4]
T. V. Antonova
Proceedings of the Steklov Institute of Mathematics, 2009, Volume 266, Number S1, Page 24

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