Interpolation by convex quadratic splines
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In this article, a quadratic spline interpolant with variable knots is presented, which preserves the monotonicity and convexity of the data, and it is shown that such a spline may not exist for fixed knots.Abstract:
Algorithms are presented for computing a quadratic spline interpolant with variable knots which preserves the monotonicity and convexity of the data. It is also shown that such a spline may not exist for fixed knots.read more
Citations
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Journal ArticleDOI
On Shape Preserving Quadratic Spline Interpolation
TL;DR: The design of algorithms for interpolating discrete data using $C^1 $-quadratic splines in such a way that the monotonicity and/or convexity of the data is preserved is discussed.
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Nonnegativity-, monotonicity-, or convexity-preserving cubic and quintic Hermite interpolation
TL;DR: In this article, the Hermite polynomials are used to preserve local positivity, monotonicity, and convexity of the data if we restrict their derivatives to satisfy constraints at the data points.
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An Algorithm for Computing a Shape-Preserving Osculatory Quadratic Spline
TL;DR: An algorithm is presented for calculating an osculatory quadratm sphne that preserves the monotonicity and convexity of the data when consmtent with the given derivatives at the data points and a discussion of pathologms that can occur when these algorithms are maplemented.
Journal Article
On Shape-Preserving Interpolation and Semi-Lagrangian Transport.
TL;DR: The Hermite cubic interpolant is improved by relaxing the strict monotonicity constraint to one suggested by Hyman at extrema, and the accuracy of the rational and piecewise quadratic Bernstein polynomial interpolants can be improved by requiring only that convexity/concavity be satisfied rather thanmonotonicity.
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On shape-preserving interpolation and semi-Lagrangian transport
TL;DR: In this article, a large number of shape-preserving methods were evaluated in terms of their relative accuracy, and the Hermite cubic interpolant with the derivative estimate of Hyman modified to produce monotonicity was shown to be the most accurate.
References
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Book
A practical guide to splines
TL;DR: This book presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines as well as specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting.
Book
Approximation of Functions
TL;DR: Possibility of approximating polynomials of best approximation with linear operators has been studied in the context of functions of one variable as mentioned in this paper, where the degree of approximation of differentiable functions has been shown to be a function of the complexity of the function.
Journal ArticleDOI
Approximation of Functions
TL;DR: Theory of Approximation of functions of a real variable as mentioned in this paper was proposed by A. F. Timan, translated by J. Cossar and J. Berry.
Journal ArticleDOI
Monotone and convex spline interpolation
Eli Passow,John A. Roulier +1 more
TL;DR: For a set of monotone (and/or convex) data, this article considered the possibility of finding a spline interpolant, of pre-determined smoothness, which is either monotonicity or convex.
Journal ArticleDOI
Algorithms for Computing Shape Preserving Spline Interpolations to Data
TL;DR: Algorithms are presented for computing a smooth piecewise polynomial interpolation which preserves the monotonicity and/or convexity of the data.