Random sampling scattered data with multivariate Bernstein polynomials

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.

Keywords

Approximation / Bernstein polynomials / Random sampling / Scattered data

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