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| Random Sampling Scattered Data with MultivariateBernstein Polynomials |
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Citation： |
Feilong CAO,Sheng XIA.Random Sampling Scattered Data with MultivariateBernstein Polynomials[J].Chinese Annals of Mathematics B,2014,35(4):607~618 |
| Page view： 1169
Net amount： 828 |
Authors： |
Feilong CAO; Sheng XIA; |
Foundation： |
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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| 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 Lp convergence for these operators are studied, respectively. |
Keywords： |
Approximation, Bernstein polynomials, Random sampling, Scattered
data |
Classification： |
41A25, 41A63, 42B08 |
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