Application of the Richardson Method in the Case of an Unknown Lower Bound of the Problem Spectrum
- 作者: Popov M.1,2, Poveschenko Y.2,3, Gasilov V.2,3, Koldoba A.4, Poveschenko T.5
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隶属关系:
- École Normale Supérieure de Lyon, CRAL (UMR CNRS 5574)
- Keldysh Institute of Applied Mathematics
- National Research Nuclear University MEPhI
- Moscow Institute of Physics and Technology
- Kurchatov Institute of Atomic Energy
- 期: 卷 10, 编号 1 (2018)
- 页面: 111-119
- 栏目: Article
- URL: https://journals.rcsi.science/2070-0482/article/view/202124
- DOI: https://doi.org/10.1134/S2070048218010106
- ID: 202124
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详细
An algorithm is presented, which enables us to use the iterative Richardson method for solving a system of linear algebraic equations with the matrix corresponding to a sign-definite selfadjoint operator, in the absence of information about the lower boundary of the spectrum of the problem. The algorithm is based on the simultaneous operation of two competing processes, the effectiveness of which is constantly analyzed. The elements of linear algebra concerning the spectral estimates, which are necessary to understand the details of the Richardson method with the Chebyshev set of parameters, are presented. The method is explained on the example of a one-dimensional equation of the elliptic type.
作者简介
M. Popov
École Normale Supérieure de Lyon, CRAL (UMR CNRS 5574); Keldysh Institute of Applied Mathematics
编辑信件的主要联系方式.
Email: hecon@mail.ru
法国, Lyon; Moscow
Yu. Poveschenko
Keldysh Institute of Applied Mathematics; National Research Nuclear University MEPhI
Email: hecon@mail.ru
俄罗斯联邦, Moscow; Moscow
V. Gasilov
Keldysh Institute of Applied Mathematics; National Research Nuclear University MEPhI
Email: hecon@mail.ru
俄罗斯联邦, Moscow; Moscow
A. Koldoba
Moscow Institute of Physics and Technology
Email: hecon@mail.ru
俄罗斯联邦, Dolgoprudny, Moscow oblast
T. Poveschenko
Kurchatov Institute of Atomic Energy
Email: hecon@mail.ru
俄罗斯联邦, Moscow