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Bounds for truncation and perturbation errors of nonuniform sampling series

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Abstract

This paper introduces a comprehensive study of truncation and perturbation errors of nonuniform sampling, interpolation, representations. We derive pointwise as well as global estimates associated with the truncated nonuniform sampling formulae. The study of the perturbation error involves the estimation of the amplitude error which results from replacing the actual samples by approximate ones, as well as the jitter error arising when alternative nodes replace the original nodes, is carried out with rigorous error bounds. Numerical and geometrical verifications of the accuracy of our estimates are exhibited.

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Acknowledgments

The authors wish to thank Alexander von Humboldt foundation for the Grant 3.4-JEM/142916 and 3.4-8131KAT/1039259.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Cairo University, P.O. Box 12613, Giza, Egypt

    M. H. Annaby

  2. Department of Mathematics, College of Arts and Sciences, Najran Universty, Najran, Saudi Arabia

    R. M. Asharabi

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  1. M. H. Annaby
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  2. R. M. Asharabi
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Correspondence to M. H. Annaby.

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Communicated by Tom Lyche.

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Annaby, M.H., Asharabi, R.M. Bounds for truncation and perturbation errors of nonuniform sampling series. Bit Numer Math 56, 807–832 (2016). https://doi.org/10.1007/s10543-015-0585-6

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  • DOI: https://doi.org/10.1007/s10543-015-0585-6

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