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Recent advances in shape preserving piecewise cubic interpolation

  • Track 8: Numerical Analysis
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Computing in the 90's (Great Lakes CS 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 507))

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Abstract

A number of recent papers have addressed the problem of constructing monotone piecewise cubic interpolants to monotone data. These have focused not only on the monotonicity of the interpolant, but also on properties such as “visual pleasure”, and optimal order error bounds. We review some of these results, and generalize them by constructing C 1 piecewise cubic polynomial interpolants to non-monotone data.These interpolants have a minimum number of changes in sign in the first derivative and approximate an underlying function and its first derivative with optimal order.

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References

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Western Michigan University, 49008, Kalamazoo, Michigan

    Thomas Sprague

Authors
  1. Thomas Sprague
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Naveed A. Sherwani Elise de Doncker John A. Kapenga

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© 1991 Springer-Verlag Berlin Heidelberg

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Sprague, T. (1991). Recent advances in shape preserving piecewise cubic interpolation. In: Sherwani, N.A., de Doncker, E., Kapenga, J.A. (eds) Computing in the 90's. Great Lakes CS 1989. Lecture Notes in Computer Science, vol 507. Springer, New York, NY. https://doi.org/10.1007/BFb0038507

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  • DOI: https://doi.org/10.1007/BFb0038507

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97628-0

  • Online ISBN: 978-0-387-34815-5

  • eBook Packages: Springer Book Archive

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