What Monte Carlo models can do and cannot do efficiently?Atanassov, E. and Dimov, I.T. (2008) What Monte Carlo models can do and cannot do efficiently? Applied Mathematical Modelling, 32 (8). pp. 1477-1500. ISSN 0307-904X Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1016/j.apm.2007.04.010 Abstract/SummaryThe question "what Monte Carlo models can do and cannot do efficiently" is discussed for some functional spaces that define the regularity of the input data. Data classes important for practical computations are considered: classes of functions with bounded derivatives and Holder type conditions, as well as Korobov-like spaces. Theoretical performance analysis of some algorithms with unimprovable rate of convergence is given. Estimates of computational complexity of two classes of algorithms - deterministic and randomized for both problems - numerical multidimensional integration and calculation of linear functionals of the solution of a class of integral equations are presented. (c) 2007 Elsevier Inc. All rights reserved.
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