On the Lebesgue constant of Berrut’s rational interpolant at equidistant nodes

Bos, Len; De Marchi, Stefano; Hormann, Kai

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On the Lebesgue constant of Berrut’s rational interpolant at equidistant nodes

Bos, Len Department of Computer Science, University of Verona, Italy
De Marchi, Stefano Department of Pure and AppliedMathematics, University of Padua, Italy
Hormann, Kai Facoltà di scienze informatiche, Università della Svizzera italiana, Svizzera

2011

7 p.

German It is well known that polynomial interpolation at equidistant nodes can give bad approximation results and that rational interpolation is a promising alternative in this setting. In this paper we confirm this observation by proving that the Lebesgue constant of Berrut’s rational interpolant grows only logarithmically in the number of interpolation nodes. Moreover, the numerical results show that the Lebesgue constant behaves similarly for interpolation at Chebyshev as well as logarithmically distributed nodes.

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