Berrut, Jean-Paul Floater, Michael S. Klein, Georges 2011-05-05 In polynomial and spline interpolation the <i>k</i>-th derivative of the interpolant, as a function of the mesh size <i>h</i>, typically converges at the rate of <i>O</i>(<i>h</i>^{<i>d</i>+1−<i>k</i>}) as <i>h</i>→0, where <i>d</i> is the degree of the polynomial or spline. In this paper we establish, in the important cases <i>k</i>=1,2, the same convergence rate for a recently proposed family of barycentric rational interpolants based on blending polynomial interpolants of degree <i>d</i>. application/pdf https://folia.unifr.ch/global/documents/301839 https://folia.unifr.ch/documents/301839/files/bary_derivs.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.apnum.2011.05.001 info:eu-repo/semantics/openAccess License undefined Applied Numerical Mathematics. - 2011, vol. 61, no. 9, p. 989-1000 Rational interpolation Barycentric form Convergence rate info:eu-repo/classification/udc/51 Convergence rates of derivatives of a family of barycentric rational interpolants http://purl.org/coar/resource_type/c_6501