Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
IMPACT FACTOR 2016: 0.783
5-year IMPACT FACTOR: 0.792
CiteScore 2016: 0.80
SCImago Journal Rank (SJR) 2015: 0.583
Source Normalized Impact per Paper (SNIP) 2015: 1.106
Mathematical Citation Quotient (MCQ) 2015: 0.43
Localization algorithms for singularities of solutions to convolution equations of the first kind
- Institute of Mathematics and Mechanics UrB RAS, Kovalevskaya st., 16, 620219 Ekaterinburg, Russia. Email: firstname.lastname@example.org
- Institute of Mathematics and Mechanics UrB RAS, Kovalevskaya st., 16, 620219 Ekaterinburg, Russia. Email: email@example.com
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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