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Improved Approximation via Use of Transformations

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Multiscale Signal Analysis and Modeling

Abstract

Function interpolation may be carried out using algebraic polynomial, splines, Fourier polynomial, rational functions, wavelets, or Sinc methods. In this chapter we describe methods for getting a more uniform approximation throughout the interval of approximation in the cases when the magnitude of the errors of interpolation is either much larger at one endpoint of the interval than the other, or when the magnitudes of the errors at endpoints are roughly the same, but differ considerably from those errors in the mid-range of the interval. We also discuss improving approximation of the derivative obtained by differentiating the constructed interpolation approximations. This chapter extends the recently obtained results of (Stenger, J Complex 25:292–302, 2009).

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Author information

Authors and Affiliations

  1. School of Computing, University of Utah, Salt Lake City, UT, 84112, USA

    Frank Stenger

  2. Mathematics Department, German University in Cairo, New Cairo City, 11835, Egypt

    Maha Youssef

  3. Radon Institute (RICAM), Austrian Academy of Science, 4040, Linz, Austria

    Jenny Niebsch

Authors
  1. Frank Stenger
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  2. Maha Youssef
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  3. Jenny Niebsch
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Corresponding author

Correspondence to Frank Stenger .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, Ohio University, Ohio University 1, Athens, 45701, Ohio, USA

    Xiaoping Shen

  2. , Department of Mathematical Sciences, DePaul University, North Kenmore Avenue 2320, Chicago, 60614, Illinois, USA

    Ahmed I. Zayed

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Stenger, F., Youssef, M., Niebsch, J. (2013). Improved Approximation via Use of Transformations. In: Shen, X., Zayed, A. (eds) Multiscale Signal Analysis and Modeling. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4145-8_2

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  • DOI: https://doi.org/10.1007/978-1-4614-4145-8_2

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-4144-1

  • Online ISBN: 978-1-4614-4145-8

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