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The average dimension of a multidimensional function for quasi-Monte Carlo estimates of an integral

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Abstract

The effective dimension of a multidimensional function was previously introduced to measure the complexity of the function with respect to the evaluation of an integral by quasi-Monte Carlo methods. For the same goal, the concept of the average dimension is introduced, which, in contrast to the effective dimension, is independent of an arbitrary confidence level.

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Authors and Affiliations

  1. Institute for Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia

    D. I. Asotsky, E. E. Myshetskaya & I. M. Sobol’

Authors
  1. D. I. Asotsky
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  2. E. E. Myshetskaya
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  3. I. M. Sobol’
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Additional information

Original Russian Text © D.I. Asotsky, E.E. Myshetskaya, I.M. Sobol’, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 12, pp. 2159–2165.

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Asotsky, D.I., Myshetskaya, E.E. & Sobol’, I.M. The average dimension of a multidimensional function for quasi-Monte Carlo estimates of an integral. Comput. Math. and Math. Phys. 46, 2061–2067 (2006). https://doi.org/10.1134/S0965542506120050

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  • DOI: https://doi.org/10.1134/S0965542506120050

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