Comonotone and coconvex rational interpolation and approximation
Comonotone and coconvex rational interpolation and approximation
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DOI：
10.1007/s11075-010-9445-2
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发表时间：
2011-09
影响因子：
2.1
通讯作者：
H. T. Nguyen;A. Cuyt;O. S. Celis
中科院分区：
文献类型：
--
作者：
H. T. Nguyen;A. Cuyt;O. S. Celis
共单调性和共凸性在一致多项式逼近和分段插值中得到了很好的理解。整体（Hermite）有理插值在某些变换下的协方差，例如取倒数，是众所周知的，但它的共单调性和共凸性的研究要少得多。在本文中，我们将展示如何在全球合理（区间）插值重心的权重可以选择，以保证不需要的极点，并在同一时间提供共单调和/或共凸插值。此外，有理（区间）插值非常适合于反映渐近行为等。
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.