Application of the Richardson Method in the Case of an Unknown Lower Bound of the Problem Spectrum
| Autor: | A. V. Koldoba, Vladimir A. Gasilov, Yu. A. Poveschenko, T. S. Poveschenko, M. V. Popov |
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| Rok vydání: | 2018 |
| Předmět: |
010102 general mathematics
Spectrum (functional analysis) MathematicsofComputing_NUMERICALANALYSIS Boundary (topology) 020206 networking & telecommunications 02 engineering and technology 01 natural sciences Chebyshev filter Upper and lower bounds Computational Mathematics Algebraic equation Matrix (mathematics) Operator (computer programming) Modeling and Simulation Linear algebra 0202 electrical engineering electronic engineering information engineering Applied mathematics 0101 mathematics Mathematics |
| Zdroj: | Mathematical Models and Computer Simulations. 10:111-119 |
| ISSN: | 2070-0490 2070-0482 |
| DOI: | 10.1134/s2070048218010106 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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