Comonotone and coconvex rational interpolation and approximation

Authors:
Hoa Thang Nguyen;Annie Cuyt;Oliver Salazar Celis
Affiliations:
Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium 2020;Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium 2020;Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium 2020
Venue:
Numerical Algorithms
Year:
2011

Citing 11
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Abstract

Comonotonicity and coconvexity are well-understood in uniform polynomial approximation and in piecewise interpolation. The covariance of a global (Hermite) rational interpolant under certain transformations, such as taking the reciprocal, is well-known, but its comonotonicity and its coconvexity are much less studied. In this paper we show how the barycentric weights in global rational (interval) interpolation can be chosen so as to guarantee the absence of unwanted poles and at the same time deliver comonotone and/or coconvex interpolants. In addition the rational (interval) interpolant is well-suited to reflect asymptotic behaviour or the like.