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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

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To link to this item DOI: 10.1016/j.apm.2007.04.010


The 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.

Item Type:Article
ID Code:15116
Uncontrolled Keywords:Monte Carlo algorithms, deterministic algorithms, multidimensional integration, integral equations, unimprovable rate of convergence , QUADRATURE-FORMULAS, INTEGRATION, ALGORITHMS

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