Title 



Sharp bounds for lebesgue constants of barycentric rational interpolation at equidistant points


Author 





Abstract 



A rough analysis of the growth of the Lebesgue constant in the case of barycentric rational interpolation at equidistant interpolation points was made in [Bos et al. 11] and [Bos et al. 12], leading to the conclusion that it only grows logarithmically. Herewe give a fine analysis, obtaining the precise growth formula 2/pi (In(n+1) + In 2 + gamma) + o(1) for the Lebesgue constant under consideration, with gamma being the Euler constant. The similarity between barycentric rational interpolation at equidistant points and polynomial interpolation at Chebyshev nodes (or the like) is remarkable. After revisiting the polynomial interpolation case in Section 1 and introducing the barycentric rational interpolation case in Section 2, tight lower and upper bound estimates are given in Section 3. These fine results could only be formulated after performing very highorder numerical experiments in exact arithmetic. In Section 4, we indicate that the result can be extended to the rational interpolants introduced by Floater and Hormann in [ Floater and Hormann 07]. Finally, the proof of the new tight bounds is detailed in Section 5.  

Language 



English


Source (journal) 



Experimental mathematics.  Place of publication unknown 

Publication 



Place of publication unknown : 2016


ISSN 



10586458


Volume/pages 



25:3(2016), p. 347354


ISI 



000373113100009


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