EFFICIENT L2 APPROXIMATION BY SPLINES

被引：8

作者：

BARROW, DL

SMITH, PW

机构：

[1] Department of Mathematics, Texas A and M University, College Station, 77843, Texas

来源：

NUMERISCHE MATHEMATIK | 1979年 / 33卷 / 01期

关键词：

Subject Classifications: primary 41A15; secondary; 41A50;

D O I：

10.1007/BF01396498

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let SNk(t) be the linear space of k-th order splines on [0, 1] having the simple knots ti determined from a fixed function t by the rule ti=t(i/N). In this paper we introduce sequences of operators {QN}N∞=1 from Ck[0, 1] to SNk(t) which are computationally simple and which, as N→∞, give essentially the best possible approximations to f and its first k-1 derivatives, in the norm of L2[0, 1]. Precisely, we show that Nk-1({norm of matrix}(f-QNf)i{norm of matrix}-dist2(f(1), SNk-1(t)))→0 for i=0, 1, ..., k-1. Several numerical examples are given. © 1979 Springer-Verlag.

引用

页码：101 / 114

页数：14

共 6 条

[1] ASYMPTOTIC PROPERTIES OF BEST L2[0,1] APPROXIMATION BY SPLINES WITH VARIABLE KNOTS [J].