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Интеллектуальная Система Тематического Исследования НАукометрических данных |
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A Flexible and Efficient Method for Solving Ill-Posed Linear Integral Equations of the First Kind for Noisy Dataстатья
- Автор: Antokhin I.I.
- Сборник: Stars: From Collapse to Collapse, Proceedings of a conference held at Special Astrophysical Observatory, Nizhny Arkhyz, Russia 3-7 October 2016
- Серия: ASP Conf. Series
- Том: 510
- Год издания: 2017
- Место издания: Astronomical Society of the Pacific San Francisco
- Первая страница: 522
- Аннотация: We propose an efficient and flexible method for solving Fredholm and Abel integral equations of the first kind, frequently appearing in astrophysics. These equations present an ill-posed problem. Our method is based on solving them on a so-called compact set of functions and/or using Tikhonov's regularization. Both approaches are non-parametric and do not require any theoretic model, apart from some very loose a priori constraints on the unknown function. The two approaches can be used independently or in a combination. The advantage of the method, apart from its flexibility, is that it gives uniform convergence of the approximate solution to the exact one, as the errors of input data tend to zero. Simulated and astrophysical examples are presented.
- Добавил в систему: Антохин Игорь Иванович