Veretennikov, AY and Veretennikov, EV (2016) On partial derivatives of multivariate Bernstein polynomials. Siberian Advances in Mathematics, 26 (4). pp. 294-305. ISSN 1055-1344
Abstract
It is shown that Bernstein polynomials for a multivariate function converge to this function along with partial derivatives provided that the latter derivatives exist and are continuous. This result may be useful in some issues of stochastic calculus.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Allerton Press, Inc., 2016. Original Russian Text ©A. Yu. Veretennikov and E. V. Veretennikova, 2015, published in Matematicheskie Trudy, 2015, Vol. 18, No. 2, pp. 22–38. This is an author produced version of a paper published in Siberian Advances in Mathematics. The final publication is available at Springer via https://doi.org/10.3103/S1055134416040039. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | multivariate Bernstein polynomial; partial derivative; convergence |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 18 Oct 2016 09:57 |
Last Modified: | 31 Jan 2019 15:32 |
Published Version: | https://doi.org/10.3103/S1055134416040039 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.3103/S1055134416040039 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:106084 |