Topic
Monotone cubic interpolation
About: Monotone cubic interpolation is a research topic. Over the lifetime, 1740 publications have been published within this topic receiving 38111 citations.
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TL;DR: Using interpolation properties of cones of general monotone functions, this paper proved the equivalence of the L (p, q ) norms of such functions and their Fourier transforms.
7 citations
TL;DR: A class of discrete Hermite interpolates in one and two independent variables is developed and explicit error bounds in @?"~ norm for the quintic and biquintic discrete Hermites are offered.
7 citations
TL;DR: In this article, the authors consider interpolation by piecewise polynomials, where the interpolation conditions are on certain derivatives of the function at certain points, specified by a finite incidence matrix E.
Abstract: We consider interpolation by piecewise polynomials, where the interpolation conditions are on certain derivatives of the function at certain points, specified by a finite incidence matrix E . Similarly the allowable discontinuities of the piecewise polynomials are specified by a finite incidence matrix F . We first find necessary conditions on ( E , F ) for the problem to be poised, that is to have a unique solution for any given data. The main result gives sufficient conditions on ( E , F ) for the problem to be poised, generalising a well-known result of Atkinson and Sharma. To this end we prove some results involving estimates of the numbers of zeros of the relevant piecewise polynomials.
7 citations
TL;DR: It is shown that interpolants exist for any true spatial data configuration and a switch to rationals provides an interpolation scheme with no restrictions.
7 citations
6 citations