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BIT Numerical Mathematics

, Volume 56, Issue 3, pp 807–832 | Cite as

Bounds for truncation and perturbation errors of nonuniform sampling series

  • M. H. Annaby
  • R. M. Asharabi
Article

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.

Keywords

Nonuniform sampling theorems Truncation  Amplitude and jitter errors 

Mathematics Subject Classification

30D10 41A05 41A30 94A20 

Notes

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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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceCairo UniversityGizaEgypt
  2. 2.Department of Mathematics, College of Arts and SciencesNajran UniverstyNajranSaudi Arabia

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