The use of the sinc-Gaussian sampling formula for approximating the derivatives of analytic functions

The use of the sinc-Gaussian sampling formula for approximating the derivatives of analytic... Numer Algor https://doi.org/10.1007/s11075-018-0548-5 ORIGINAL PAPER The use of the sinc-Gaussian sampling formula for approximating the derivatives of analytic functions Rashad M. Asharabi Received: 28 July 2017 / Accepted: 9 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The sinc-Gaussian sampling formula is used to approximate an analytic function, which satisfies a growth condition, using only finite samples of the func- tion. The error of the sinc-Gaussian sampling formula decreases exponentially with −1/2 −αN respect to N, i.e., N e ,where α is a positive number. In this paper, we extend this formula to allow the approximation of derivatives of any order of a function from two classes of analytic functions using only finite samples of the function itself. The theoretical error analysis is established based on a complex analytic approach; the convergence rate is also of exponential type. The estimate of Tanaka et al. (Jpan J. Ind. Appl. Math. 25, 209–231 2008) can be derived from ours as an immediate corol- lary. Various illustrative examples are presented, which show a good agreement with our theoretical analysis. Keywords Sinc approximation · Sampling series · Approximating derivatives · Gaussian convergence factor · Error bounds · Entire http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Numerical Algorithms Springer Journals

The use of the sinc-Gaussian sampling formula for approximating the derivatives of analytic functions

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Computer Science; Numeric Computing; Algorithms; Algebra; Theory of Computation; Numerical Analysis
ISSN
1017-1398
eISSN
1572-9265
D.O.I.
10.1007/s11075-018-0548-5
Publisher site
See Article on Publisher Site

Abstract

Numer Algor https://doi.org/10.1007/s11075-018-0548-5 ORIGINAL PAPER The use of the sinc-Gaussian sampling formula for approximating the derivatives of analytic functions Rashad M. Asharabi Received: 28 July 2017 / Accepted: 9 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The sinc-Gaussian sampling formula is used to approximate an analytic function, which satisfies a growth condition, using only finite samples of the func- tion. The error of the sinc-Gaussian sampling formula decreases exponentially with −1/2 −αN respect to N, i.e., N e ,where α is a positive number. In this paper, we extend this formula to allow the approximation of derivatives of any order of a function from two classes of analytic functions using only finite samples of the function itself. The theoretical error analysis is established based on a complex analytic approach; the convergence rate is also of exponential type. The estimate of Tanaka et al. (Jpan J. Ind. Appl. Math. 25, 209–231 2008) can be derived from ours as an immediate corol- lary. Various illustrative examples are presented, which show a good agreement with our theoretical analysis. Keywords Sinc approximation · Sampling series · Approximating derivatives · Gaussian convergence factor · Error bounds · Entire

Journal

Numerical AlgorithmsSpringer Journals

Published: May 29, 2018

References

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