On the Linear Independence of Multivariate i?-Splines. II: Complete Configurations
نویسندگان
چکیده
The first part of this paper is concerned with global characterizations of both the multivariate ß-spline and the multivariate truncated power function as smooth piecewise polynomials. In the second part of the paper we establish combinatorial criteria for the linear independence of multivariate ß-splines corresponding to certain configurations of knot sets.
منابع مشابه
Phase II monitoring of multivariate simple linear profiles with estimated parameters
In some applications of statistical process monitoring, a quality characteristic can be characterized by linear regression relationships between several response variables and one explanatory variable, which is referred to as a “multivariate simple linear profile.” It is usually assumed that the process parameters are known in Phase II. However, in most applications, this assumption is viola...
متن کاملA Necessary and Sufficient Condition for the Linear Independence of the Integer Translates of a Compactly Supported Distribution
Given a multivariate compactly supported distribution φ, we derive here a necessary and sufficient condition for the global linear independence of its integer translates. This condition is based on the location of the zeros of φ̂ = The Fourier-Laplace transform of φ. The utility of the condition is demonstrated by several examples and applications, showing in particular, that previous results on...
متن کاملAssessment of canal configuration in mandibular anterior teeth extracted in the city of Isfahan and patients treatedin Endodontics Department of Isfahan Faculty of Dentistry
Assessment of canal configuration in mandibular anterior teeth extracted in the city of Isfahan and patients treated in Endodontics Department of Isfahan Faculty of Dentistry Dr. SM. Hasheminiya*- Dr. SM. Hosseini Harandi** - Dr. M. Narimani** *- Assistant professor of Endodontics Dept.- Faculty of Dentistry - Isfahan University of Medical Sciences. ** - Dentist. Background and aim: Recogni...
متن کاملON AN INDEPENDENT RESULT USING ORDER STATISTICS AND THEIR CONCOMITANT
Let X1;X2;...;Xn have a jointly multivariate exchangeable normal distribution. In this work we investigate another proof of the independence of X and S2 using order statistics. We also assume that (Xi ; Yi); i =1; 2;...; n; jointly distributed in bivariate normal and establish the independence of the mean and the variance of concomitants of order statistics.
متن کاملWhat is a multivariate spline?
The various concepts and ideas that have contributed to univariate spline theory are considered with a view to finding a suitable definition of a multivariate spline. In this way, an overview of the existing more or less complete univariate spline theory is given along with a survey of some of the high points of the current research in multivariate splines. My very first paper dealt with multiv...
متن کامل