IMPROVED ERROR-BOUNDS FOR NEAR-MINIMAX APPROXIMATIONS

被引：1

作者：

ELLIOTT, D

PHILLIPS, GM

机构：

[1] UNIV TASMANIA,DEPT MATH,HOBART,TAS 7005,AUSTRALIA

[2] UNIV ST ANDREWS,INST MATH,ST ANDREWS KY16 9SS,FIFE,SCOTLAND

来源：

BIT | 1991年 / 31卷 / 02期

关键词：

ERROR BOUNDS; DIVIDED DIFFERENCES; NEAR MINIMAX POLYNOMIAL APPROXIMATIONS;

D O I：

10.1007/BF01931286

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Given f is-an-element-of C(n + 1)[-1,1], a polynomial p(n), of degree less-than-or-equal-to n, is said to be near-minimax if (*) parallel-to f - p(n) parallel-to infinity = 2-n\f(n+1)(xi)\/(n+1)!, for some xi is-an-element-of (-1,1). For three sets of near-minimax approximations, by considering the form of the error parallel-to f - p(n) parallel-to infinity in terms of divided differences, it is shown that better upper and lower bounds can be found than those given by (*).

引用

页码：262 / 275

页数：14

共 9 条

[1]

Bernstein S., 1926, LECONS PROPRIETES EX

[2] ERROR-ESTIMATES FOR LEAST-SQUARES APPROXIMATION BY POLYNOMIALS [J].