N. A. Serdyukova
Published 2012-08-15Version 1
In the present paper a behavior of the "average case" approximation complexity for d-parametric random fields of tensor-type is studied. It was shown in [Lifshits and Tulyakova, 2006] that for a given approximation accuracy level the complexity of approximation increases exponentially, as d tends to infinity; that is the curse of dimensionality is observed. In this paper a technique allowing obtaining sharp asymptotic expressions for the approximation complexity is developed and such an expression is obtained.
Comments: The original version in Russian was submitted on 15.01.2007 to Theor. Veroyatnost. i Primenen. and published as "Zavisimost slozhnosti approximacii sluchajnyh polej ot rasmernosti". The extended English translation is published in Theory Probab. Appl. (2010) 54:2, 272-284, arXiv: http://arxiv.org/abs/math/0701058
Journal: Theor. Veroyatnost. i Primenen. (2009) 54:2, 256-270
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