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A survey of average case complexity for linear multivariate problems |
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| Authors: | G W Wasilkowski H Wo?niakowski |
| Institution: | (1) University of Kentucky, Lexington, KY 40506, USA;(2) Columbia University, New York, NY 10027, USA;(3) University of Warsaw, 02-097 Warsaw, Poland |
| 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. Dedicated to the 50th anniversary of the journal. The text was submitted by the authors in English. |
| Keywords: | and phrases" target="_blank"> and phrases average case setting minimal error Wiener measure complexity Hilbert space linear nultivariate problem Wiener sheet Banach space tractability tensor product weighted approximation |
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