Compactly supported positive definite radial functions

Abstract  We provide criteria for positive definiteness of radial functions with compact support. Based on these criteria we will produce
a series of positive definite and compactly supported radial functions, which will be very useful in applications. The simplest
ones arecut-off polynomials, which consist of a single polynomial piece on [0, 1] and vanish on [1, ∞). More precisely, for any given dimensionn and prescribedC

^k
smoothness, there is a function inC

^k
(ℝ
ⁿ
), which is a positive definite radial function with compact support and is a cut-off polynomial as a function of Euclidean
distance. Another example is derived from odd-degreeB-splines.

• Content Type Journal Article
• DOI 10.1007/BF03177517
• Authors
  
  
  • Zongmin Wu, Fudan University Department of Mathematics 200433 Shanghai China
  
  

• Journal Advances in Computational Mathematics
• Online ISSN 1572-9044
• Print ISSN 1019-7168




• Journal Volume Volume 4




• Journal Issue Volume 4, Number 1 / December, 1995

Published by

Original source : http://www.springerlink.com/content/tm636718128620...