A constructive approach to nodal splines
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In this article, the authors show how to represent the Hermite Martensen spline recursively and explicitly in terms of the B-spline by using the famous Marsden identity.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2007-06-01 and is currently open access. It has received 8 citations till now. The article focuses on the topics: Spline interpolation & Hermite spline.read more
Citations
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Error estimates for discrete spline interpolation
Fengmin Chen,Patricia J. Y. Wong +1 more
TL;DR: In this paper, a class of discrete spline interpolates in one and two independent variables is developed and explicit error bounds in the? ∞ norm are derived for the quintic and biquintic discrete splines interpolates.
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Histopolating splines
TL;DR: In this paper, the authors considered the problem of constructing a spline H"n(f) of degree n of an integrable function f, where n is the number of degrees in the function f.
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Martensen splines and finite-part integrals
TL;DR: It is proved that a sequence of Martensen splines, based on locally uniform meshes, satisfies the sufficient conditions required by the uniform convergence theorem and the quadrature rules based on such splines are constructed.
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Smoothness and error bounds of Martensen splines
TL;DR: This paper aims to clarify how well the Martensen splines M f approximate smooth functions on compact intervals.
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Nodal splines on compact intervals
TL;DR: In this paper, it was shown that the nodal spline interpolation operator on compact intervals can be regarded as a discretized version of the Martensen operator, which can be seen as an alternative perspective on the nodals.
References
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Book
Spline Functions: Basic Theory
TL;DR: The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences.
Book ChapterDOI
Contributions to the Problem of Approximation of Equidistant Data by Analytic Functions
TL;DR: The polynomial central interpolation (PCI) method as mentioned in this paper is a popular method for computing intermediate values of a known analytic function F(x) to the same accuracy to which the ordinates are known.
Journal ArticleDOI
An identity for spline functions with applications to variation-diminishing spline approximation☆
Book
Progress in approximation theory
Paul Nevai,Allan Pinkus +1 more
TL;DR: Agarwal and G.Leviatan as discussed by the authors gave a characterization of the classical orthogonal poly-nominals, R.Kahn best L-approximations, K.Rohwer entire functions associated with eq where q is of slower than polynomial growth, MAtteia on the norm of the best approximation operator.