title: On solution of two-sided vector equation in tropical algebra
metadata.name: dc.contributor.author
metadata.value: Krivulin, Nikolai K.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-05-18T21:48:51Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-05-18T21:48:51Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-05
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Krivulin N.K. On solution of two-sided vector equation in tropical algebra. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2023, vol. 10 (68), issue 2, pp. 236–248. https://doi.org/10.21638/spbu01.2023.205 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2023.205
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/41481
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The problem of solving, in the context of tropical mathematics, a vector equation with
  two given matrices and unknown vectors, each part of which has the form of a product
  of one of the matrices and an unknown vector, is considered. Such an equation, which
  has unknown vectors on either side of the equal sign, is often called a two-sided equation.
  A new procedure for solving the two-sided equation is proposed based on minimizing a
  certain distance function between vectors of tropical vector spaces that are generated by
  the columns of each of the matrices. As a result of the procedure, a pair of vectors is
  obtained, which provides a minimum distance between spaces and the value of the distance
  itself. If the equation has solutions, then the resulting vectors are the solution to the
  equation. Otherwise, these vectors define a pseudo-solution that minimizes the deviation
  of one side of the equation from the other. The execution of the procedure consists in
  constructing a sequence of vectors that are pseudo-solutions of the two-sided equation in
  which the left and right sides are alternately replaced by constant vectors. Unlike the wellknown
  alternating algorithm, in which the corresponding inequalities are solved one by one
  instead of equations, the proposed procedure uses a different argument, looks simpler, and
  allows one to establish natural criteria for completing calculations. If the equation has no
  solutions, the procedure also finds a pseudo-solution and determines the value of the error
  associated with it, which can be useful in solving approximation problems.
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 10; Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: idempotent semifield
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: tropical vector space
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: generalized metric
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: two-sided vector equation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: iterative computational procedure
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: pseudo-solution
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On solution of two-sided vector equation in tropical algebra
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 236-248.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/41481/1/236-248.pdf
resources.format: Adobe PDF
resources.size: 349,23 kB