نتایج جستجو برای: polynomial spline

تعداد نتایج: 110206  

Journal: :The Annals of Mathematical Statistics 1969

Journal: :Journal of Computational and Applied Mathematics 2013

Abdellah Lamnii Fatima Oumellal Jaoud Dabounou

In this paper simple quartic trigonometric polynomial blending functions, with a tensionparameter, are presented. These type of functions are useful for constructing trigonometricB´ezier curves and surfaces, they can be applied to construct continuous shape preservinginterpolation spline curves with shape parameters. To better visualize objects and graphics atension parameter is included. In th...

1966
Carl de Boor Robert E. Lynch

0. Introduction. It is the purpose of this note to show that the several minimum properties of odd degree polynomial spline functions [4, 18] all derive from the fact that spline functions are representers of appropriate bounded linear functionals in an appropriate Hilbert space. (These results were first announced in Notices, Amer. Math. Soc., 11 (1964) 681.) In particular, spline interpolatio...

2012
Yogesh Gupta Manoj Kumar

Spline methods provide an important tool to solve singularly perturbed boundary value problems. The present paper gives a comprehensive review of computational methods based on splines used in the solution of various classes of singularly perturbed problems such as self adjoint, linear, non-linear, semi-linear, quasi-linear, singular, single parameter and multi parameter. The spline based numer...

2003
JIANHUA Z. HUANG

In this paper we develop a general theory of local asymptotics for least squares estimates over polynomial spline spaces in a regression problem. The polynomial spline spaces we consider include univariate splines, tensor product splines, and bivariate or multivariate splines on triangulations. We establish asymptotic normality of the estimate and study the magnitude of the bias due to spline a...

1993
Felix P. Abramovich

We establish the asymptotical equivalence between L-spline smoothing and kernel estimation. The equivalent kernel is used to derive the asymptotic mean squared error of the L-smoothing spline estimator. The paper extends the corresponding results for polynomial spline smoothing.

2006
Lan Xue Lijian Yang LIJIAN YANG

A flexible nonparametric regression model is considered in which the response depends linearly on some covariates, with regression coefficients as additive functions of other covariates. Polynomial spline estimators are proposed for the unknown coefficient functions, with optimal univariate mean square convergence rate under geometric mixing condition. Consistent model selection method is also ...

2011
Jean-Paul Berrut Michael S. Floater Georges Klein

In polynomial and spline interpolation the k-th derivative of the interpolant, as a function of the mesh size h, typically converges at the rate of O(hd+1−k) as h → 0, where d is the degree of the polynomial or spline. In this paper we establish, in the important cases k = 1, 2, the same convergence rate for a recently proposed family of barycentric rational interpolants based on blending polyn...

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