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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

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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   

  1. 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   

  1. School of Mathematical Science, Tianjin Normal University, Tianjin 300387, China
  • Received:2016-07-04 Online:2017-08-20 Published:2017-08-03

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Lp(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 Lp(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
[1] HARRIS L A. Lagrange polynomials, reproducing kernels and cubature in two dimensions[J]. Journal of Approximation Theory, 2015, 195: 43-56.
[2] 谢庭藩,周颂平. 实变函数逼近论[M].杭州:杭州大学出版社,1998. XIE Tingfan, ZHOU Songping. Approximation theory of real functions[M]. Hangzhou: Hangzhou University Press, 1998.
[3] SZABADOS J, VÉRTESI P. Interpolation of Functions[M]. Singapore: World Scientific, 1990.
[4] SZABAGOS J, VÉRTESI P. A Survey on mean convergence of interpolatory processes[J]. Journal of Computational and Applied Mathematics, 1992, 43: 3-18.
[5] VARMA A K, PRASAD J. An analogue of a problem of P. Erdös and E. Feldheim on Lp convergence of interpolatory processes[J]. Journal of Approximation Theory, 1989, 56(2): 225-240.
[6] NEVAI P, XU Y. Mean convergence of Hermite-interpolation[J]. Journal of Approximation Theory, 1994, 77(3): 282-304.
[7] VÉRTESI P, XU Y. Mean convergence of Hermite interpolation revisited[J]. Acta Mathematica Hungarica, 1995, 69(3): 185-210.
[8] SHI Yingguang. On Hermite interpolation[J]. Journal of Approximation Theory, 2000, 105(1): 49-86.
[9] XU Guiqiao. On weak tractability of the Smolyak algorithm for approximation problems[J]. Journal of Approximation Theory, 2014, 192: 347-361.
[10] SHI Yingguang. Convergence of Hermite-Féjer type interpolation of higher order on an arbitrary system of nodes[J]. Journal of Approximation Theory, 2003, 123(2): 173-187.
[11] DEVORE R A, LORENTZ G G. Constructive approximation[M]. Berlin: Springer, 1993.
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