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2017 | OriginalPaper | Chapter

Linear Barycentric Rational Interpolation with Guaranteed Degree of Exactness

Author : Jean-Paul Berrut

Published in: Approximation Theory XV: San Antonio 2016

Publisher: Springer International Publishing

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Abstract

In recent years, linear barycentric rational interpolants, introduced in 1988 and improved in 2007 by Floater and Hormann, have turned out to be among the most efficient infinitely smooth interpolants, in particular with equispaced points. In the present contribution, we introduce a new way of obtaining linear barycentric rational interpolants with relatively high orders of convergence. The basic idea is to modify the interpolant with equal weights of 1988 to force it to interpolate exactly the monomials up to a certain degree. This is obtained by modifying a few weights at each extremity of the interval of interpolation. Numerical experience demonstrates that the method is indeed able to interpolate with much higher orders than the original 1988 interpolant and in a very stable way.

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next chapter Approximation by Splines on Piecewise Conic Domains
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Metadata
Title
Linear Barycentric Rational Interpolation with Guaranteed Degree of Exactness
Author
Jean-Paul Berrut
Copyright Year
2017
Book
Approximation Theory XV: San Antonio 2016

Print ISBN: 978-3-319-59911-3

Electronic ISBN: 978-3-319-59912-0

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-59912-0_1

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