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Polynomial approximations of multivariate smooth functions from quasi-random data

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Abstract

We improve a Monte Carlo algorithm which computes accurate approximations of smooth functions on multidimensional Tchebychef polynomials by using quasi-random sequences. We first show that the convergence of the previous algorithm is twice faster using these sequences. Then, we slightly modify this algorithm to make it work from a single set of random or quasi-random points. This especially leads to a Quasi-Monte Carlo method with an increased rate of convergence for numerical integration.

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Authors and Affiliations

  1. ISITV, Université de Toulon et du Var, Avenue G, Pompidou BP, 56 - 83262, La Valette du Var, Cedex, France

    Sylvain Maire

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  1. Sylvain Maire
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Maire, S. Polynomial approximations of multivariate smooth functions from quasi-random data. Statistics and Computing 14, 333–336 (2004). https://doi.org/10.1023/B:STCO.0000039482.91826.ce

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  • DOI: https://doi.org/10.1023/B:STCO.0000039482.91826.ce

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