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Sampling by incomplete cosine expansion of the sinc function: Application to the Voigt/complex error function

Author

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  • Abrarov, S.M.
  • Quine, B.M.

Abstract

A new sampling methodology based on an incomplete cosine expansion series is presented as an alternative to the traditional sinc function approach. Numerical integration shows that this methodology is efficient and practical. Applying the incomplete cosine expansion we obtain a rational approximation of the complex error function that with the same number of the summation terms provides an accuracy exceeding the Weideman’s approximation accuracy by several orders of the magnitude. Application of the expansion results in an integration consisting of elementary function terms only. Consequently, this approach can be advantageous for accurate and rapid computation.

Suggested Citation

  • Abrarov, S.M. & Quine, B.M., 2015. "Sampling by incomplete cosine expansion of the sinc function: Application to the Voigt/complex error function," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 425-435.
  • Handle: RePEc:eee:apmaco:v:258:y:2015:i:c:p:425-435
    DOI: 10.1016/j.amc.2015.01.072
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    Cited by:

    1. Abrarov, Sanjar M. & Quine, Brendan M., 2018. "A rational approximation of the Dawson’s integral for efficient computation of the complex error function," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 526-543.
    2. Sanjar M. Abrarov & Rehan Siddiqui & Rajinder K. Jagpal & Brendan M. Quine, 2022. "A Two-Domain MATLAB Implementation for Efficient Computation of the Voigt/Complex Error Function," Mathematics, MDPI, vol. 10(19), pages 1-14, September.
    3. S. M. Abrarov & B. M. Quine & R. Siddiqui & R. K. Jagpal, 2019. "A Single-Domain Implementation of the Voigt/Complex Error Function by Vectorized Interpolation," Earth Science Research, Canadian Center of Science and Education, vol. 8(2), pages 1-52, February.

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