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 article, the authors studied the existence, uniqueness and convergence of discrete cubic splines which interpolate to a given function at one interior point of each mesh interval, including continuous periodic cubic spline.
Abstract: In the present paper we study the existence, uniqueness and convergence of discrete cubic spline which interpolate to a given function at one interior point of each mesh interval. Our result in particular, includes the interpolation problems concerning continuous periodic cubic splines and discrete cubic splines with boundary conditions considered respectively in Meir and Sharma (1968) and Lyche (1976) for the case of equidistant knots.
29 citations
TL;DR: The shapes of the positive and convex data are under discussion of the proposed spline solutions of the C 2 rational cubic spline.
29 citations
TL;DR: In this paper, the authors identify admissible slopes at data points of various C 1 interpolants which ensure a desirable shape, in turn for the following function classes commonly used for shape-preserving interpolations: monotone polynomials, C 1 -monotone piecewise polynomial, convex polynomorphisms, parametric cubic curves and rational functions.
Abstract: In many applications, interpolation of experimental data exhibiting some geometric property such as nonnegativity, monotonicity or convexity is unacceptable unless the interpolant reflects these characteristics. This paper identifies admissible slopes at data points of variousC 1 interpolants which ensure a desirable shape. We discuss this question, in turn for the following function classes commonly used for shape preserving interpolations: monotone polynomials,C 1 monotone piecewise polynomials, convex polynomials, parametric cubic curves and rational functions.
29 citations
28 citations
TL;DR: This paper characterize MPH curves in R2,1 by the roots of the hodographs of their complexified spine curves, and presents two schemes for this interpolation problem: one is a subdivision scheme using direct C1 interpolation and the other is a two step scheme using a new concept, C1/2 interpolation.
28 citations