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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, Number 4, Pages 3–19 (Mi ivm1314)  
This article is cited in 4 scientific papers (total in 4 papers)

A survey of average case complexity for linear multivariate problems

G. W. Wasilkowskia, H. Woźniakowskibc

a University of Kentucky, Department of Computer Science
b Columbia University, Department of Computer Science
c University of Warsaw, Institute of Applied Mathematics
Full-text PDF (269 kB) Citations (4)
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Abstract: We survey recent results on the average case complexity for linear multivariate problems. Our emphasis is on problems defined on spaces of functions of $d$ variables with large $d$. We present the sharp order of the average case complexity for a number of linear multivariate problems as well as necessary and sufficient conditions for the average case complexity not to be exponential in $d$.
Keywords: average case setting, minimal error, Wiener measure, complexity, Hilbert space, linear nultivariate problem, Wiener sheet, Banach space, tractability, tensor product, weighted approximation.
Received: 02.08.2008
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2009, Volume 53, Issue 4, Pages 1–14
DOI: https://doi.org/10.3103/S1066369X0904001X
Bibliographic databases:
UDC: 517.988+519.218
Language: Russian
Citation: G. W. Wasilkowski, H. Woźniakowski, “A survey of average case complexity for linear multivariate problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 4, 3–19; Russian Math. (Iz. VUZ), 53:4 (2009), 1–14
Citation in format AMSBIB
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\by G.~W.~Wasilkowski, H.~Wo{\'z}niakowski
\paper A~survey of average case complexity for linear multivariate problems
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2009
\issue 4
\pages 3--19
\mathnet{http://mi.mathnet.ru/ivm1314}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2581468}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2009
\vol 53
\issue 4
\pages 1--14
\crossref{https://doi.org/10.3103/S1066369X0904001X}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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