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An Exact Order of Discrepancy of the Smolyak Grid and Some General Conclusions in the Theory of Numerical Integration

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Abstract

This paper examines the relationship between the degree of uniformity of distribution of grids, including Smolyak grids, with the intention of choosing weights to obtain efficient quadrature formulas.

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Notes

  1. Here and below, the notation c(…) indicates positive values, generally speaking different in different expressions, and depending only on the parameters in brackets. For positive A and arbitrary B, the notation B≪ α,β,… A means |B|≤c(α,β,…)A, and for positive A and B the notation A≍ α,β,… B means A≪ α,β,… B≪ α,β,… A.

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Authors and Affiliations

  1. Institute of Theoretical Mathematics and Scientific Computations, Eurasian National University, 5 Munaitpassov Street, Astana, 010008, Kazakhstan

    Nurlan Nauryzbayev & Nurlan Temirgaliyev

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  1. Nurlan Nauryzbayev
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  2. Nurlan Temirgaliyev
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Correspondence to Nurlan Temirgaliyev.

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Communicated by Henryk Woźniakowski.

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Nauryzbayev, N., Temirgaliyev, N. An Exact Order of Discrepancy of the Smolyak Grid and Some General Conclusions in the Theory of Numerical Integration. Found Comput Math 12, 139–172 (2012). https://doi.org/10.1007/s10208-012-9116-x

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  • DOI: https://doi.org/10.1007/s10208-012-9116-x

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