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Polynomial convergence order of stochastic Bernstein approximation.
- Source :
-
Advances in Computational Mathematics . Feb2020, Vol. 46 Issue 1, p1-14. 14p. - Publication Year :
- 2020
-
Abstract
- Recently, authors of Wu et al. (Adv. Comput. Math. 38:187-205, 2013) studied a Bernstein polynomial approximation scheme based on stochastic sampling and obtained a sixth-order moment estimate for the underlying random variable in terms of the modulus of continuity. In the current paper, we employ a new technique and establish estimates for all the even-order moments. Our work gives a strong indication that the probabilistic convergence rate of the stochastic Bernstein approximation is exponential with respect to the modulus of continuity, which we leave as a conjecture at the end of the paper. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10197168
- Volume :
- 46
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Advances in Computational Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 141689710
- Full Text :
- https://doi.org/10.1007/s10444-020-09742-w