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Numerical Algorithms
Published in: Numerical Algorithms 4/2021

29-06-2020 | Original Paper

Accurate sampling formula for approximating the partial derivatives of bivariate analytic functions

Authors: R. M. Asharabi, J. Prestin

Published in: Numerical Algorithms | Issue 4/2021

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Abstract

The bivariate sinc-Gauss sampling formula is introduced in Asharabi and Prestin (IMA J. Numer. Anal. 36:851–871, 2016) to approximate analytic functions of two variables which satisfy certain growth condition. In this paper, we apply this formula to approximate partial derivatives of any order for entire and holomorphic functions on an infinite horizontal strip domain using only finitely many samples of the function itself. The rigorous error analysis is carried out with sharp estimates based on a complex analytic approach. The convergence rate of this technique will be of exponential type, and it has a high accuracy in comparison with the accuracy of the bivariate classical sampling formula. Several computational examples are exhibited, demonstrating the exactness of the obtained results.
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Metadata
Title
Accurate sampling formula for approximating the partial derivatives of bivariate analytic functions
Authors
R. M. Asharabi
J. Prestin
Publication date
29-06-2020
Publisher
Springer US
Published in
Numerical Algorithms / Issue 4/2021
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-020-00939-0

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