基于第四类Chebyshev多项式零点的Lagrange插值多项式逼近

doi:10.6040/j.issn.1671-9352.0.2016.315

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (8): 10-16.doi: 10.6040/j.issn.1671-9352.0.2016.315

基于第四类Chebyshev多项式零点的Lagrange插值多项式逼近

张艳艳,闫超

天津师范大学数学科学学院, 天津 300387

收稿日期:2016-07-04 出版日期:2017-08-20 发布日期:2017-08-03
作者简介:张艳艳(1973— ),女,硕士,讲师,研究方向为随机计算与数据分析. E-mail:yanyanzhang1973@163.com
基金资助:
国家自然科学基金青年科学基金项目(11401436)

Approximation of lagrange interpolation polynomials based on the fourth Chebyshev nodes

ZHANG Yan-yan, YAN Chao

School of Mathematical Science, Tianjin Normal University, Tianjin 300387, China

Received:2016-07-04 Online:2017-08-20 Published:2017-08-03

摘要/Abstract

摘要： 给出了最大框架下基于第四类Chebyshev结点组的Lagrange插值多项式在最大范数下逼近一类解析函数时的精确误差。又针对L^p(p>1)范数,给出了插值函数对该类解析函数类的逼近误差的强渐近阶。

关键词: Lagrange插值, 最大框架, Chebyshev多项式, 函数逼近

Abstract: This paper first provides the exact approximation errors for an analytic function class under the maximum norm based on the Lagrange interpolation polynomials with the fourth Chebyshev nodes in the worst setting. As for the norm of L^p(p>1), the corresponding strong asymptotic order for that kind of analytic function class is obtained.

Key words: Lagrange interpolation, worst case setting, function approximation, Chebyshev polynomial

中图分类号:

O174.41

张艳艳,闫超. 基于第四类Chebyshev多项式零点的Lagrange插值多项式逼近[J]. 山东大学学报（理学版）, 2017, 52(8): 10-16.

ZHANG Yan-yan, YAN Chao. Approximation of lagrange interpolation polynomials based on the fourth Chebyshev nodes[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 10-16.

参考文献

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基于第四类Chebyshev多项式零点的Lagrange插值多项式逼近

Approximation of lagrange interpolation polynomials based on the fourth Chebyshev nodes

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