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http://hdl.handle.net/11701/15553
Полная запись метаданных
Поле DC | Значение | Язык |
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dc.contributor.author | Krivulin, Nikolai K. | - |
dc.contributor.author | Romanova, Elizaveta Yu. | - |
dc.date.accessioned | 2019-05-24T11:04:33Z | - |
dc.date.available | 2019-05-24T11:04:33Z | - |
dc.date.issued | 2019-06 | - |
dc.identifier.citation | Krivulin N.K., Romanova E.Yu. On rank-one approximation of positive matrices using methods of tropical optimization. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 2, pp. 208–220. | en_GB |
dc.identifier.other | https://doi.org/10.21638/11701/spbu01.2019.203 | - |
dc.identifier.uri | http://hdl.handle.net/11701/15553 | - |
dc.description.abstract | In the paper, an approach to the problem of rank-one approximation of positive matrices in the Chebyshev metric in logarithmic scale is developed based on the application of methods of tropical optimization. The theory and methods of tropical optimization constitute one of the areas of tropical mathematics that deals with semirings and semifields with idempotent addition and their applications. For many practically important problems, methods of tropical optimization allow finding a complete solution explicitly in a closed form. In this work, the approximation problem under consideration is reduced to multidimensional tropical optimization problem, which has a known solution in the general case. A new solution to the problem in the case when the matrix has no zero columns or rows is proposed and represented in a more simple form. On the basis of this result, a new complete solution of the problem of rank-one approximation of positive matrices is developed. To illustrate the results obtained, an example of the solution of the approximation problem for an arbitrary positive matrix of the second order is given in analytical form. | en_GB |
dc.description.sponsorship | Работа выполнена при финансовой поддержке РФФИ в рамках научного проекта № 18-010- 00723. | en_GB |
dc.language.iso | ru | en_GB |
dc.publisher | St Petersburg State University | en_GB |
dc.relation.ispartofseries | Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 6 (64); Issue 2 | - |
dc.subject | tropical mathematics | en_GB |
dc.subject | tropical optimization | en_GB |
dc.subject | max-algebra | en_GB |
dc.subject | rank-one matrix approximation | en_GB |
dc.subject | log-Chebyshev distance | en_GB |
dc.title | On rank-one approximation of positive matrices using methods of tropical optimization | en_GB |
dc.type | Article | en_GB |
Располагается в коллекциях: | Issue 2 |
Файлы этого ресурса:
Файл | Описание | Размер | Формат | |
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208-220.pdf | 336,42 kB | Adobe PDF | Просмотреть/Открыть |
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