title: A simplified criterion for quasi-polynomial tractability of approximation of random elements and its applications
metadata.name: dc.contributor.author
metadata.value: Khartov, Alexey Andreevich
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-06-17T05:39:08Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-06-17T05:39:08Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-06
metadata.lang: -
metadata.name: dc.identifier.issn
metadata.value: 0885064X
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/2305
metadata.lang: -
metadata.name: dc.description
metadata.value: Conferences: International Workshop "Information-Based Complexity and Model Selection", France, Paris,
   (April 9 - 10, 2015); International Conference "Information-based complexity", Poland, Bedlewo (April 26 - May 2, 2015);
metadata.lang: en_GB
metadata.name: dc.description.abstract
metadata.value: We study approximation properties of sequences of centered random elements Xd, d∈N, with values in separable Hilbert spaces. We focus on sequences of tensor product-type random elements, which have covariance operators of corresponding tensor product form. The average case approximation complexity nXd(ε) is defined as the minimal number of evaluations of arbitrary linear functionals that is needed to approximate Xd with relative 2-average error not exceeding a given threshold ε∈(0,1). The growth of nXd(ε) as a function of ε^(−1) and d determines whether a sequence of corresponding approximation problems for Xd, d∈N, is tractable or not. Different types of tractability were studied in the paper by Lifshits et al. (J. Complexity, 2012), where for each type the necessary and sufficient conditions were found in terms of the eigenvalues of the marginal covariance operators. We revise the criterion of quasi-polynomial tractability and provide a simplified version. We illustrate our result by applying it to random elements corresponding to tensor products of squared exponential kernels. We also extend a recent result of Xu (2014) concerning weighted Korobov kernels.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: RFBR grant 13-01-00172; SPbGU grant 6.38.672.2013; Grant of Scientific school  NSh-2504.2014.1.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: Elsevier
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Journal of Complexity;34
metadata.lang: -
metadata.name: dc.subject
metadata.value: Linear tensor product approximation problems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Average case approximation complexity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Quasi-polynomial tractability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Random fields
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: A simplified criterion for quasi-polynomial tractability of approximation of random elements and its applications
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: Manuscript.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/2305/1/Manuscript.pdf
resources.format: Adobe PDF
resources.description: Manuscript
resources.size: 302,93 kB