title: Rank-one approximation of positive matrices based on methods of tropical mathematics
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: 2018-07-12T19:36:19Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-07-12T19:36:19Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Krivulin N.K., Romanova E.Yu. Rank-one approximation of positive matrices based on methods of tropical mathematics. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 2, pp. 256–269.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.206
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/10403
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Low-rank matrix approximation finds wide application in the analysis of big data, in recommendation
  systems on the Internet, for approximate solution of some equations in mechanics,
  and in other fields. In the paper, a method for approximating positive matrices by
  matrices of unit rank is proposed on the basis of minimization of log-Chebyshev distance.
  The approximation problem is reduced to an optimization problem that has a compact representation
  in terms of an idempotent semifield that uses the operation of taking maximum
  in the role of addition, and is often called the max-algebra. The necessary definitions and
  preliminary results of tropical mathematics are given, on the basis of which the solution
  of the original problem is derived. Using methods and results of tropical optimization, all
  the positive matrices which provide the minimum of approximation error are obtained in
  explicit form. A numerical example that illustrates the application of the proposed rank-one
  approximation method is considered.
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 5(63); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: tropical mathematics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: idempotent semifield
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: Rank-one approximation of positive matrices based on methods of tropical mathematics
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 06-Krivulin.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/10403/1/06-Krivulin.pdf
resources.format: Adobe PDF
resources.size: 345,58 kB