title: An estimate of average case approximation complexity for tensor degrees of random processes
metadata.name: dc.contributor.author
metadata.value: Kravchenko, Аleksandr А.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Khartov, Alexey A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-02-16T19:10:00Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-02-16T19:10:00Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Kravchenko А. А., Khartov A.A. An estimate of average case approximation complexity for tensor degrees of random processes. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 4, pp. 580–592.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.403
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/35105
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We consider random fields that are tensor degrees of a random process of second order
  with continuous covariance function. The average case approximation complexity of a random
  field is defined as the minimal number of evaluations of linear functionals needed to
  approximate the field with relative 2-average error not exceeding a given threshold. In the
  present paper we estimate the growth of average case approximation complexity of random
  field for arbitrary high its parametric dimension and for arbitrary small error threshold.
  Under rather weak assumptions on the spectrum of covariance operator of the generating
  random process, we obtain necessary and sufficient condition that the average case approximation
  complexity has the upper estimate of a special form. We show that this condition
  covers a wide class of cases and the order of the estimate of the average case approximation
  complexity coincides with the order of its asymptotics, which were obtained earlier in the
  paper by Lifshits and Tulyakova.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work of A.A.Khartov was supported by the joint Russian Foundation for Basic Research and
  German Research Foundation (grant no. 20-51-12004).
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 8 (66); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: average case approximation complexity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: random field
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: tensor degree
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: high dimension
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: tractability
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: An estimate of average case approximation complexity for tensor degrees of random processes
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 580-592.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/35105/1/580-592.pdf
resources.format: Adobe PDF
resources.size: 310,62 kB