scholarly journals Penalized hyperbolic-polynomial splines

2021 ◽  
Vol 118 ◽  
pp. 107159
Author(s):  
Rosanna Campagna ◽  
Costanza Conti
Keyword(s):  
Polynomial Splines ◽  
Hyperbolic Polynomial

Polynomial splines over hierarchical T-meshes

2008 ◽  
Vol 70 (4) ◽  
pp. 76-86 ◽  
Author(s):  
Jiansong Deng ◽  
Falai Chen ◽  
Xin Li ◽  
Changqi Hu ◽  
Weihua Tong ◽  
...  
Keyword(s):  
Polynomial Splines

Non-polynomial splines approach to the solution of sixth-order boundary-value problems

2008 ◽  
Vol 195 (1) ◽  
pp. 270-284 ◽  
Author(s):  
Siraj-ul-Islam ◽  
Ikram A. Tirmizi ◽  
Fazal-i-Haq ◽  
M. Azam Khan
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Sixth Order ◽  
Polynomial Splines

scholarly journals Real Zeros of a Class of Hyperbolic Polynomials with Random Coefficients

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Mina Ketan Mahanti ◽  
Amandeep Singh ◽  
Lokanath Sahoo
Keyword(s):  
Random Variables ◽  
Random Coefficients ◽  
Expected Number ◽  
Hyperbolic Polynomial ◽  
Gaussian Random Variables ◽  
Hyperbolic Polynomials ◽  
Asymptotic Value ◽  
Real Zeros ◽  
Number Of Real Zeros

We have proved here that the expected number of real zeros of a random hyperbolic polynomial of the formy=Pnt=n1a1cosh⁡t+n2a2cosh⁡2t+⋯+nnancosh⁡nt, wherea1,…,anis a sequence of standard Gaussian random variables, isn/2+op(1). It is shown that the asymptotic value of expected number of times the polynomial crosses the levely=Kis alson/2as long asKdoes not exceed2neμ(n), whereμ(n)=o(n). The number of oscillations ofPn(t)abouty=Kwill be less thann/2asymptotically only ifK=2neμ(n), whereμ(n)=O(n)orn-1μ(n)→∞. In the former case the number of oscillations continues to be a fraction ofnand decreases with the increase in value ofμ(n). In the latter case, the number of oscillations reduces toop(n)and almost no trace of the curve is expected to be present above the levely=Kifμ(n)/(nlogn)→∞.

Non-periodic Polynomial Splines

2015 ◽  
pp. 51-85
Author(s):  
Amir Z. Averbuch ◽  
Pekka Neittaanmäki ◽  
Valery A. Zheludev
Keyword(s):  
Polynomial Splines

scholarly journals A characterization of supersmoothness of multivariate splines

2020 ◽  
Vol 46 (5) ◽  
Author(s):  
Michael S. Floater ◽  
Kaibo Hu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Order ◽  
Maximal Order ◽  
Spline Functions ◽  
Multivariate Splines ◽  
The Finite Element Method ◽  
Polynomial Splines ◽  
Element Method

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.

Continuous delay estimation with polynomial splines

2006 ◽  
Vol 120 (5) ◽  
pp. 3112-3112
Author(s):  
Gianmarco Pinton ◽  
Gregg Trahey
Keyword(s):  
Delay Estimation ◽  
Polynomial Splines ◽  
Continuous Delay

scholarly journals Interval estimation of trigonometrical splines

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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