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

页码：97 / 110

页数：14

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