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Approximation of additive random fields based on standard information: Average case and probabilistic settings
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. St Petersburg State University, Russia.
University of Orleans, France.
2015 (English)In: Journal of Complexity, ISSN 0885-064X, E-ISSN 1090-2708, Vol. 31, no 5, 659-674 p.Article in journal (Refereed) Published
Abstract [en]

We consider approximation problems for tensor product and additive random fields based on standard information in the average case setting. We also study the probabilistic setting of the mentioned problem for tensor products. The main question we are concerned with in this paper is "How much do we loose by considering standard information algorithms against those using general linear information?" For both types of the fields, the error of linear algorithms has been studied in great detail; however, the power of standard information was not addressed so far, which we do here. Our main result is that in most interesting cases there is no more than a logarithmic loss in approximation error when information is being restricted to the standard one. The results are obtained by randomization techniques. (C) 2015 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2015. Vol. 31, no 5, 659-674 p.
Keyword [en]
Approximation complexity; Additive random fields; Gaussian processes; Standard information; Tensor product random fields
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-121423DOI: 10.1016/j.jco.2015.05.002ISI: 000360250000001OAI: oai:DiVA.org:liu-121423DiVA: diva2:855144
Note

Funding Agencies|RFBR [13-01-00172]; SPbSU [6.38.672.2013]

Available from: 2015-09-18 Created: 2015-09-18 Last updated: 2016-01-26

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Lifshits, Mikhail
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Mathematical Statistics Faculty of Science & Engineering
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