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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 3, Pages 351–362
DOI: https://doi.org/10.7868/S004446691603008X (Mi zvmmf10354) 		 
This article is cited in 8 scientific papers (total in 8 papers)

On the principal and strictly particular solutions to infinite systems

O. F. Ivanova, N. N. Pavlov, F. M. Fedorov

North–East Federal University, ul. Belinskogo 58, Yakutsk, 677000, Russia
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DOI: https://doi.org/10.7868/S004446691603008X
Abstract: The concepts of the principal solution to infinite systems of linear algebraic equations and the reduction method are defined more precisely. The principal solution, if it exists, is a strictly particular solution to the infinite system. If the reduction method is convergent, then it necessarily converges to Kramer’s determinant; however, Kramer’s determinant is not always a solution to the infinite system. To confirm the obtained results, analytical and numerical solutions of specific infinite system are considered.
Key words: infinite systems of linear algebraic equations, Gaussian elimination, Kramer's determinant, Gaussian systems, reduction method in the narrow and wide sense.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 3047
Received: 26.07.2015
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 3, Pages 343–353
DOI: https://doi.org/10.1134/S0965542516030088
Bibliographic databases:
Document Type: Article
UDC: 519.61
Language: Russian
Citation: O. F. Ivanova, N. N. Pavlov, F. M. Fedorov, “On the principal and strictly particular solutions to infinite systems”, Zh. Vychisl. Mat. Mat. Fiz., 56:3 (2016), 351–362; Comput. Math. Math. Phys., 56:3 (2016), 343–353
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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