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: Differentiable, two-dimensional, piecewise polynomial cubic prewavelets of particularly small compact support are designed, given in closed form, and provide stable, orthogonal decompositions of L2 (R2) .
Abstract: Dedicated to Professor M. J. D. Powell on the occasion
of his sixty-fifth birthday and his retirement.
In this paper, we design differentiable, two-dimensional, piecewise polynomial cubic prewavelets of particularly small compact support. They are given in closed form, and provide stable, orthogonal decompositions of L
2
(R
2
) . In particular, the splines we use in our prewavelet constructions give rise to stable bases of spline spaces that contain all cubic polynomials, whereas the more familiar box spline constructions cannot reproduce all cubic polynomials, unless resorting to a box spline of higher polynomial degree.
6 citations
TL;DR: For smooth and visualizing pleasant curve, a positivity preserving interpolation by using alternative spline that is, cubic trigonometric spline with two shape parameters was constructed in this article.
Abstract: For smooth and visualizing pleasant curve, we construct a positivity preserving interpolation by using alternative spline that is, cubic trigonometric spline with two shape parameters. In the description of the cubic trigonometric spline interpolant, positivity is preserved everywhere and has a unique representation for the positivity. We develop a constraints on the shape parameters to preserve the shape of the positive data in the view of smooth and pleasant positive curve by trigonometric interpolant. The degree of smoothness of the under discussion scheme is $C^1.$
Keywords: Cubic Trigonometric Spline; Shape Preservation; Interpolation; Positivity; Positive Data; Shape parameters.
2010 Mathematics Subject Classification 65D05, 65D07, 65D17, 65D18, 65U07.
6 citations
TL;DR: In this article, the coefficients of a quadrature formula for Fourier integrals over a finite interval are determined, and the integrand is interpolated by a cubic spline of defect 1 with equidistant nodes, the exponential factor being treated as a weighting function.
Abstract: The coefficients of a quadrature formula for Fourier integrals over a finite interval are determined. The integrand is interpolated by a cubic spline of defect 1 with equidistant nodes, the exponential factor being treated as a weighting function.
6 citations
01 Jan 2012
TL;DR: In this article, a weighted rational cubic spline interpolation with linear denominator is proposed to preserve the monotonicity and convexity of given monotonic data and given convex data and a proper choice of the parameter i and the weight coefficient to guarantee shape preservation is given.
Abstract: A weighted rational cubic spline interpolation is constructed using two kinds of rational cubic spline with linear denominator. The degree of smoothness of the interpolation function is C 2 in the interpolating interval when the parameters satisfy a continuous system. The interpolant can preserve the monotonicity and convexity of given monotonic data and convex data, and a proper choice of the parameter i and the weight coefficient to guarantee shape preservation is given. Several examples are supplied to support the practical value of the method.
6 citations
TL;DR: A new generalization of fuzzy finite state machines, fuzzy transformation semigroups and their relationship is provided and it is shown that the composition of strong cfsm homomorphism is also strong.
Abstract: This paper provides a new generalization of fuzzy finite state machines, fuzzy transformation semigroups and their relationship. Consider a cubic structure, we introduce cubic finite state machines, cubic transformation semigroups, cubic successor, cubic exchange properties cubic subsystems, cubic submachines, cubic q-twins, cubic retrievable and study fundamental properties of them. We provide relationship between cubic q-twins and a cubic q-related. We provide a characterization of a cubic retrievable. We define cfsm homomorphism and investigated related properties. We show that the composition of strong cfsm homomorphism is also strong. We also define cubic transformation semigroup and it related properties. We define cts homomorphism and its properties.
6 citations