Convergence rates of derivatives of a family of barycentric rational interpolants

• Autores: Jean Paul Berrut, Michael S. Floater, Georges Klein
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 61, Nº. 9, 2011, págs. 989-1000
• Idioma: inglés
• DOI: 10.1016/j.apnum.2011.05.001
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• Resumen

  • 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 proposed family of barycentric rational interpolants based on blending polynomial interpolants of degree d.