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Convergence of linear barycentric rational interpolation for analytic functions

Güttel, Stefan ; Klein, Georges

In: SIAM Journal on Numerical Analysis, 2012, vol. 50, no. 5, p. 2560–2580

Polynomial interpolation to analytic functions can be very accurate, depending on the distribution of the interpolation nodes. However, in equispaced nodes and the like, besides being badly conditioned, these interpolants fail to converge even in exact arithmetic in some cases. Linear barycentric rational interpolation with the weights presented by Floater and Hormann can be viewed as blended...