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: In this paper, the problem of interpolation by a complete spline of 2n − 1 degree given in B-spline representation is studied, and explicit formulas for the first n and the last n coefficients of Bspline decomposition are found.
Abstract: We study the problem of interpolation by a complete spline of 2n − 1 degree given in B-spline representation. Explicit formulas for the first nand the last ncoefficients of B-spline decomposition are found. It is shown that other B-spline coefficients can be computed as a solution of a banded system of an equitype linear equations.
8 citations
TL;DR: In this article, the convergence of Hermite and Hermite-Fejer interpolation polynomials of higher order at the zeros of Freud orthogonal polynomial on the real line was investigated.
8 citations
TL;DR: The sufficient conditions for convex, monotone, or positive approximation are given and some examples are provided to illustrate shape-preserving properties of the splines.
8 citations
TL;DR: In this article, a method for interpolating planar data points by cubic G 2 splines is presented, where a spline is composed of polynomial segments that interpolate two data points, tangent directions and curvatures at these points.
Abstract: In this paper a method for interpolating planar data points by cubic G 2 splines is presented. A spline is composed of polynomial segments that interpolate two data points, tangent directions and curvatures at these points. Necessary and sufficient, purely geometric conditions for the existence of such a polynomial interpolant are derived. The obtained results are extended to the case when the derivative directions and curvatures are not prescribed as data, but are obtained by some local approximation or implied by shape requirements. As a result, the G 2 spline is constructed entirely locally.
8 citations