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An efficient and flexible Abel-inversion method for noisy dataстатья
Статья опубликована в высокорейтинговом журнале
Статья опубликована в журнале из списка Web of Science и/или ScopusДата последнего поиска статьи во внешних источниках: 2 ноября 2016 г.
- Автор: Antokhin I.I.
- Журнал: Monthly Notices of the Royal Astronomical Society
- Том: 463
- Номер: 2
- Год издания: 2016
- Издательство: Oxford Journals, Oxford University Press
- Местоположение издательства: Oxford, UK, England
- Первая страница: 2079
- Последняя страница: 2084
- DOI: 10.1093/mnras/stw2111
- Аннотация: We propose an efficient and flexible method for solving Abel integral equation of the first kind, frequently appearing in many fields of astrophysics, physics, chemistry, engineering and applied sciences. This equation represents an ill-posed problem, thus solving it requires some kind of regularization. Our method is based on solving the equation on a so-called compact set of functions and/or using Tikhonov's regularization. A priory constraints on the unknown function defining a compact set, are very loose and can be set using simple physical considerations and common sense. Tikhonov's regularization on itself does not require any a priori constraints on the unknown function and can be used independently or in combination with a priori constraints. Various target degrees of smoothness of the unknown function may be set, as required by the problem at hand. The advantage of the method, apart from its flexibility, is that it warrants uniform convergence of the approximate solution to the exact solution, as the errors of input data tend to zero. An example of astrophysical application of the method is given.
- Добавил в систему: Антохин Игорь Иванович