Well-conditioned, stable and infinitely smooth interpolation in arbitrary nodes is by no means a trivial task, even in the univariate setting considered here; already the most important case, equispaced points, is not obvious. Certain approaches have nevertheless experienced significant developments in the last decades. In this paper we review one of them, linear barycentric rational interpolation, as well as some of its applications. © 2013 Elsevier B.V. All rights reserved.
Berrut, J. P., & Klein, G. (2014). Recent advances in linear barycentric rational interpolation. Journal of Computational and Applied Mathematics, 259(PART A), 95–107. https://doi.org/10.1016/j.cam.2013.03.044