MULTIVARIATE INTERPOLATION IN ODD-DIMENSIONAL EUCLIDEAN SPACES USING MULTIQUADRICS

被引：48

作者：

BUHMANN, MD ^{[1
]}

机构：

[1] UNIV CAMBRIDGE,DEPT APPL MATH & THEORET PHYS,CAMBRIDGE CB3 9EW,ENGLAND

来源：

CONSTRUCTIVE APPROXIMATION | 1990年 / 6卷 / 01期

关键词：

AMS classification: Primary 41A05; 41A63; 41A25; Secondary; 41A30; Multiquadrics; Multivariate approximation; Multivariate interpolation; Orders of convergence; Polynomial precision; Radial basis functions;

D O I：

10.1007/BF01891407

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let {Mathematical expression} or {Mathematical expression}. Given f:ℛn→ℛ, we establish convergence orders of interpolation where the cardinal function x with x(j)=δ0 j is a linear combination of integer shifts, of a fast decaying function {Mathematical expression}N ⊂F″being a finite subset. If n is odd and {Mathematical expression}, we find convergence orders of hn+1, whereas for {Mathematical expression}, convergence orders of hn-1 are obtained when n≥3 is odd. © 1990 Springer-Verlag New York Inc.

引用

页码：21 / 34

页数：14

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