QUASI-INTERPOLANTS FROM SPLINE INTERPOLATION OPERATORS

被引：5
|
作者：
SMITH, PW
WARD, JD
机构：
[1] TEXAS A&M UNIV SYST,DEPT MATH,COLLEGE STN,TX 77843
[2] IMSL INC,HOUSTON,TX
来源：
CONSTRUCTIVE APPROXIMATION | 1990年 / 6卷 / 01期
关键词：
AMS classification: Primary 41A15; Secondary; 41A05; Poisson summation formula; Quasi-interpolation formulae; Toeplitz matrix;
D O I：
10.1007/BF01891410
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For bi-infinite Toeplitz matrices, it is easy to see that the kth partial sum of the Neumann series reproduces polynomials of order k There is no guarantee, however, that the spectral radius is less than 1. A principal result of this paper is to show that for the spline interpolation Toeplitz case the spectral radius is less than 1 when A is invertible and the main diagonal is the central diagonal. This is not true for all totally positive Toeplitz matrices as shown by an example in Section 2. © 1990 Springer-Verlag New York Inc.
引用
收藏
页码：97 / 110
页数：14
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