In this paper we extend and generalise an interative approach for
constructing the Hermite interpolant introduced by Cirillo and Hormann (2018)
for the Floater-Hormann family of interpolants. In particular, we apply that
scheme to produce an effective barycentric rational trigonometric Hermite
interpolant using the basis function of the interpolant introduced by Berrut
(1988). In order to give an easy construction of such an interpolant we compute
the differentation matrix analytically and we conclude with various examples
and a numerical study of the rate of convergence at equidistant nodes

Elefante, Giacomo

English

arXiv

In this work we construct an Hermite interpolant starting from basis
functions that satisfy a Lagrange property. In fact, we extend and generalise
an iterative approach, introduced by Cirillo and Hormann (2018) for the
Floater-Hormann family of interpolants. Secondly, we apply this scheme to
produce an effective barycentric rational trigonometric Hermite interpolant at
general ordered nodes using as basis functions the ones of the trigonometric
interpolant introduced by Berrut (1988). For an easy computational
construction, we calculate analytically the differentation matrix. Finally, we
conclude with various examples and a numerical study of the rate of convergence
at equidistant nodes and conformally mapped nodes

arXiv.org e-Print Archive

A barycentric trigonometric Hermite interpolant via an iterative
  approach

In this work we construct an Hermite interpolant starting from basis functions that satisfy a Lagrange property. In fact, we extend and generalise an iterative approach, introduced by Cirillo and Hormann (2018) for the Floater–Hormann family of interpolants. Secondly, we apply this scheme to produce an effective barycentric rational trigonometric Hermite interpolant at general ordered nodes using as basis functions the ones of the trigonometric interpolant introduced by Berrut (1988). For an easy computational construction, we calculate analytically the differentiation matrix. Finally, we conclude with various examples and a numerical study of the convergence at equidistant nodes and conformally mapped nodes

A barycentric trigonometric Hermite interpolant via an iterative approach

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