The Conditioning of a Linear Barycentric Rational Interpolant

Jean-Paul Berrut ()
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Jean-Paul Berrut: University of Fribourg, Department of Mathematics

A chapter in Realization and Model Reduction of Dynamical Systems, 2022, pp 23-37 from Springer

Abstract: Abstract We study what a referee has asked us to call the “second Berrut rational interpolant”, introduced thirty years ago, which is linear in the interpolated function values and converges exponentially when the nodes are conformal images of Chebyshev points. We show that the Lebesgue constant for this interpolant grows just logarithmically with the number of nodes under reasonable assumptions, extending results of Bos et al. in 2013 for the corresponding first interpolant.

Keywords: Linear rational interpolation; Conditioning; Logarithmic growth; Lebesgue constant; Conformally shifted nodes (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-95157-3_2

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DOI: 10.1007/978-3-030-95157-3_2

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