NDLI: Sampling scattered data with Bernstein polynomials: stochastic and deterministic error estimates

Content Provider	Springer Nature Link
Author	Sun, Xingping Ma, Limin Wu, Zongmin
Copyright Year	2011
Abstract	Viewing the classical Bernstein polynomials as sampling operators, we study a generalization by allowing the sampling operation to take place at scattered sites. We utilize both stochastic and deterministic approaches. On the stochastic side, we consider the sampling sites as random variables that obey some naturally derived probabilistic distributions, and obtain Chebyshev type estimates. On the deterministic side, we incorporate the theory of uniform distribution of point sets (within the framework of Weyl’s criterion) and the discrepancy method. We establish convergence results and error estimates under practical assumptions on the distribution of the sampling sites.
Ending Page	205
Page Count	19
Starting Page	187
File Format	PDF
ISSN	10197168
e-ISSN	15729044
Journal	Advances in Computational Mathematics
Issue Number	1
Volume Number	38
Language	English
Publisher	Springer US
Publisher Date	2011-09-30
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Discrepancy Summability Numeric Computing Erdős and Turán inequality Mathematics Theory of Computation Bernstein polynomials Multidimensional problems (should also be assigned at least one other classification number in this section) Scattered data Uniform distribution Weyl’s criterion Algebra Calculus of Variations and Optimal Control; Optimization Sampling Rate of convergence, degree of approximation Chebyshev inequality
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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