In: Journal of computational and applied mathematics, 2019, vol. 349, p. 292-301
Barycentric rational Floater–Hormann interpolants compare favourably to classical polynomial interpolants in the case of equidistant nodes, because the Lebesgue constant associated with these interpolants grows logarithmically in this setting, in contrast to the exponential growth experienced by polynomials. In the Hermite setting, in which also the first derivatives of the interpolant are...
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In: Numerical Algorithms, 2011, vol. 57, no. 1, p. 67-81
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In: BIT Numerical Mathematics, 2012, vol. 52, no. 2, p. 407-424
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In: Mathematics of Computation, 2012, vol. 82, no. 284, p. 2273-2292
The barycentric rational interpolants introduced by Floater and Hormann in 2007 are “blends” of polynomial interpolants of fixed degree d. In some cases these ratio- nal functions achieve approximation of much higher quality than the classical poly- nomial interpolants, which, e.g., are ill-conditioned and lead to Runge’s phenomenon if the interpolation nodes are equispaced. For such...
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In: Bit Numerical Mathematics, 2012, vol. 52, no. 2, p. 407-424
Linear interpolation schemes very naturally lead to quadrature rules. Introduced in the eighties, linear barycentric rational interpolation has recently experienced a boost with the presentation of new weights by Floater and Hormann. The corresponding interpolants converge in principle with arbitrary high order of precision. In the present paper we employ them to construct two linear 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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