Non-periodic Polynomial Splines

Abstract We consider spline functions over simplicial meshes in $\mathbb {R}^{n}$ ℝ n . We assume that the spline pieces join together with some finite order of smoothness but the pieces themselves are infinitely smooth. Such splines can have extra orders of smoothness at a vertex, a property known as supersmoothness, which plays a role in the construction of multivariate splines and in the finite element method. In this paper, we characterize supersmoothness in terms of the degeneracy of spaces of polynomial splines over the cell of simplices sharing the vertex, and use it to determine the maximal order of supersmoothness of various cell configurations.

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Continuous delay estimation with polynomial splines

The Journal of the Acoustical Society of America ◽

10.1121/1.4787607 ◽

2006 ◽

Vol 120 (5) ◽

pp. 3112-3112

Author(s):

Gianmarco Pinton ◽

Gregg Trahey

Keyword(s):

Delay Estimation ◽

Polynomial Splines ◽

Continuous Delay

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Interval estimation of trigonometrical splines

MATEC Web of Conferences ◽

10.1051/matecconf/201929203001 ◽

2019 ◽

Vol 292 ◽

pp. 03001

Author(s):

I.G. Burova ◽

E.G. Ivanova ◽

V.A. Kostin

Keyword(s):

Function Approximation ◽

Order Approximation ◽

Spline Approximation ◽

Approximation Error ◽

Interval Estimation ◽

Polynomial Splines ◽

Third Order ◽

Variation Range ◽

Local Spline ◽

Third Order Approximation

Quite often, it is necessary to quickly determine variation range of the function. If the function values are known at some points, then it is easy to construct the local spline approximation of this function and use the interval analysis rules. As a result, we get the area within which the approximation of this function changes. It is necessary to take into account the approximation error when studying the obtained area of change of function approximation. Thus, we get the range of changing the function with the approximation error. This paper discusses the features of using polynomial and trigonometrical splines of the third order approximation to determine the upper and lower boundaries of the area (domain) in which the values of the approximation are contained. Theorems of approximation by these local trigonometric and polynomial splines are formulated. The values of the constants in the estimates of the errors of approximation by the trigonometrical and polynomial splines are given. It is shown that these constants cannot be reduced. An algorithm for constructing the variation domain of the approximation of the function is described. The results of the numerical experiments are given.

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