CHEBYSHEV INTERPOLATION AND QUADRATURE FORMULAS OF VERY HIGH DEGREE

被引：4

作者：

SALZER, HE

机构：

[1] Brooklyn, NY

来源：

COMMUNICATIONS OF THE ACM | 1969年 / 12卷 / 05期

关键词：

Chebyshev interpolation; Chebyshev points; Chebyshev polynomials; Chebyshev quadrature; Chebyshev zeros; definite integrals; interpolation; quadrature;

D O I：

10.1145/362946.362980

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

All the zeros x2 i = 1(1)2m of the Chebyshev polynomials T2(x), m = 0(1)n, are found recursively just by taking n2n-1 real square roots. For interpolation or integration of (x), given (x2), only x2 is needed to calculate (a) the (2m - 1)-th degree Lagrange interpolation polynomial, and (b) the definite integral over [-1, 1], either with or without the weight function (1 - x2)-1/2 the former being exact for (x) of degree 2m+1 - 1. © 1969, ACM. All rights reserved.

引用

页码：271 / &