In: BIT Numerical Mathematics, 2012, vol. 52, no. 2, p. 407-424
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In: Journal of Computational and Applied Mathematics, 2014, vol. 259, Part A, p. 95–107
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...
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In: Applied Numerical Mathematics, 2011, vol. 61, no. 9, p. 989-1000
In polynomial and spline interpolation the k-th derivative of the interpolant, as a function of the mesh size h, typically converges at the rate of O(hd+1−k) as h→0, where d is the degree of the polynomial or spline. In this paper we establish, in the important cases k=1,2, the same convergence rate for a recently...
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