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

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Abstract

The sinc-Gaussian sampling formula is used to approximate an analytic function, which satisfies a growth condition, using only finite samples of the function. The error of the sinc-Gaussian sampling formula decreases exponentially with respect to N, i.e., N− 1/2e−αN, 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 corollary. Various illustrative examples are presented, which show a good agreement with our theoretical analysis.

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Acknowledgements

The author would like to thank the anonymous reviewers for their valuable comments and Professor M.H. Annaby for his comments and critical reading of the manuscript.

Funding

The author gratefully acknowledges the support by the Deanship of Scientific Research, Najran University, Saudi Arabia, for grant NU/ESCI/15/007.

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Authors and Affiliations

  1. Department of Mathematics, College of Arts and Sciences, Najran University, Najran, Saudi Arabia

    Rashad M. Asharabi

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  1. Rashad M. Asharabi
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Correspondence to Rashad M. Asharabi.

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Asharabi, R.M. The use of the sinc-Gaussian sampling formula for approximating the derivatives of analytic functions. Numer Algor 81, 293–312 (2019). https://doi.org/10.1007/s11075-018-0548-5

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  • DOI: https://doi.org/10.1007/s11075-018-0548-5

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