Approximation Properties of Chebyshev Polynomials in the Legendre Norm

Author:

Niu Cuixia,Liao Huiqing,Ma Heping,Wu Hua

Abstract

In this paper, we present some important approximation properties of Chebyshev polynomials in the Legendre norm. We mainly discuss the Chebyshev interpolation operator at the Chebyshev–Gauss–Lobatto points. The cases of single domain and multidomain for both one dimension and multi-dimensions are considered, respectively. The approximation results in Legendre norm rather than in the Chebyshev weighted norm are given, which play a fundamental role in numerical analysis of the Legendre–Chebyshev spectral method. These results are also useful in Clenshaw–Curtis quadrature which is based on sampling the integrand at Chebyshev points.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Reference32 articles.

1. Numerical Methods in Scientific Computing, Volume I

2. Error bounds for approximation in Chebyshev points

3. Spectral methods

4. Chebyshev and Fourier Spectral Methods;Boyd,2001

5. Spectral Methods;Canuto,2007

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A Model-Free Optimal Control Method;SoutheastCon 2024;2024-03-15

2. Polynomial Sequences and Their Applications;Mathematics;2022-12-16

3. Dynamics of Fractional Chaotic Systems with Chebyshev Spectral Approximation Method;International Journal of Applied and Computational Mathematics;2022-05-19

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3