Geodesic
A~survey of average case complexity for linear multivariate problems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2009), pp. 3-19

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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. 
@article{IVM_2009_4_a0,
     author = {G. W. Wasilkowski and H. Wo\'zniakowski},
     title = {A~survey of average case complexity for linear multivariate problems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--19},
     publisher = {mathdoc},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_4_a0/}
}
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G. W. Wasilkowski; H. Woźniakowski. A~survey of average case complexity for linear multivariate problems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2009), pp. 3-19. http://geodesic.mathdoc.fr/item/IVM_2009_4_a0/