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Random sampling scattered data with multivariate Bernstein polynomials

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Abstract

In this paper, the multivariate Bernstein polynomials defined on a simplex are viewed as sampling operators, and a generalization by allowing the sampling operators to take place at scattered sites is studied. Both stochastic and deterministic aspects are applied in the study. On the stochastic aspect, a Chebyshev type estimate for the sampling operators is established. On the deterministic aspect, combining the theory of uniform distribution and the discrepancy method, the rate of approximating continuous function and L p convergence for these operators are studied, respectively.

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Authors and Affiliations

  1. Department of Mathematics, China Jiliang University, Hangzhou, 310018, China

    Feilong Cao & Sheng Xia

Authors
  1. Feilong Cao
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  2. Sheng Xia
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Corresponding author

Correspondence to Feilong Cao.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 61272023, 61101240) and the Innovation Foundation of Post-Graduates of Zhejiang Province (No. YK2011070).

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Cao, F., Xia, S. Random sampling scattered data with multivariate Bernstein polynomials. Chin. Ann. Math. Ser. B 35, 607–618 (2014). https://doi.org/10.1007/s11401-014-0844-x

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  • DOI: https://doi.org/10.1007/s11401-014-0844-x

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