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, a weighted second-order (quadratic) interpolation technique is proposed to eliminate the oscillation phenomena manifested in the numerical Eulerian-Lagrangian solution of the convection dispersion equation in natural coordinates when sharp fronts of concentration occur.
10 citations
19 May 2012
TL;DR: A novel envelope fitting method based on the optimized piecewise cubic Hermite (OPCH) interpolation is developed, taking the difference between extreme as the cost function, chaos particle swarm optimization (CPSO) method is used to optimize the derivatives of the interpolation nodes.
Abstract: Empirical mode decomposition (EMD) is an adaptive method for analyzing non-stationary time series derived from linear and nonlinear systems. But the upper and lower envelopes fitted by cubic spline (CS) interpolation may often occur overshoots. In this paper, a novel envelope fitting method based on the optimized piecewise cubic Hermite (OPCH) interpolation is developed. Taking the difference between extreme as the cost function, chaos particle swarm optimization (CPSO) method is used to optimize the derivatives of the interpolation nodes. The flattest envelope with the optimized derivatives can overcome the overshoots well. Some numerical experiments conclude this paper, and comparisons are carried out with the classical EMD.
10 citations
TL;DR: In this paper, a basic algorithm for merging two adjacent cubic pieces of a given composite cubic curve is suggested, which is combined with a standard interpolating scheme to approximate a sequence of data points by a composite cubic of few pieces.
Abstract: A basic algorithm for merging two adjacent cubic pieces of a given composite cubic curve is suggested here. As a typical application, it is combined with a standard interpolating scheme to approximate a sequence of data points by a composite cubic of few pieces.
10 citations
TL;DR: In this article, the authors prove several comparison theorems for difference equations and discuss their application to spline interpolation at knots, and discuss the application of the comparison theorem for spline spline at knots.
10 citations
TL;DR: Cubic spline least squares fitting algorithms for continous functions and functions with jump discontinuities were developed for X-ray photoelectric cross sections in this paper, and the cubic spline coefficients for incoherent and coherent scattering cross sections for elements from sodium through cobalt were reported for energies from 1 to 150 keV, and when two interior knots (three regions) are used they yield accuracies better than those obtined by a single cubic polynomial.
10 citations