Application of the Richardson Method in the Case of an Unknown Lower Bound of the Problem Spectrum
- Autores: Popov M.1,2, Poveschenko Y.2,3, Gasilov V.2,3, Koldoba A.4, Poveschenko T.5
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Afiliações:
- 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
- Edição: Volume 10, Nº 1 (2018)
- Páginas: 111-119
- Seção: Article
- URL: https://journals.rcsi.science/2070-0482/article/view/202124
- DOI: https://doi.org/10.1134/S2070048218010106
- ID: 202124
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Resumo
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.
Sobre autores
M. Popov
École Normale Supérieure de Lyon, CRAL (UMR CNRS 5574); Keldysh Institute of Applied Mathematics
Autor responsável pela correspondência
Email: hecon@mail.ru
França, Lyon; Moscow
Yu. Poveschenko
Keldysh Institute of Applied Mathematics; National Research Nuclear University MEPhI
Email: hecon@mail.ru
Rússia, Moscow; Moscow
V. Gasilov
Keldysh Institute of Applied Mathematics; National Research Nuclear University MEPhI
Email: hecon@mail.ru
Rússia, Moscow; Moscow
A. Koldoba
Moscow Institute of Physics and Technology
Email: hecon@mail.ru
Rússia, Dolgoprudny, Moscow oblast
T. Poveschenko
Kurchatov Institute of Atomic Energy
Email: hecon@mail.ru
Rússia, Moscow