title: On rank-one approximation of positive matrices using methods of tropical optimization
metadata.name: dc.contributor.author
metadata.value: Krivulin, Nikolai K.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Romanova, Elizaveta Yu.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-05-24T11:04:33Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-05-24T11:04:33Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.203
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15553
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РФФИ в рамках научного проекта № 18-010- 00723.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 6 (64); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: tropical mathematics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: tropical optimization
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: max-algebra
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: rank-one matrix approximation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: log-Chebyshev distance
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On rank-one approximation of positive matrices using methods of tropical optimization
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 208-220.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15553/1/208-220.pdf
resources.format: Adobe PDF
resources.size: 336,42 kB