二元组合型三角插值多项式的收敛阶

吉林大学学报(工学版) ›› 2002, Vol. ›› Issue (1): 52-56.

二元组合型三角插值多项式的收敛阶

张淑婷, 王淑云, 何甲兴

吉林大学数学科学学院, 吉林, 长春, 130025

收稿日期:2001-08-11 出版日期:2002-01-25

Convergence Order of Double Variate Combination Trigonometric Interpolation Polynomials

ZHANG Shu-ting, WANG Shu-yun, HE Jia-xing

College of Mathematics Science, Jilin University, Changchun 130025, China

Received:2001-08-11 Online:2002-01-25

摘要/Abstract

摘要： 构造了一个二元组合型三角插值多项式算子T_nm(f;x,y),使得T_nm(f;x,y)不仅对于任意被插值的二元连续周期函数都能在全平面上一致收敛,且具有最佳收敛阶。

关键词: 二元组合型算子, 一致收敛, 最佳收敛阶

Abstract: In this paper,double variate trigonometric interpolation polynomials are constructed to make the arbitrary continuous periodic function f(x,y) with period 2π,converge on f(x,y) and be uniform on total plane.The convergence order is the best.

Key words: double variate combination operator, trigonometric interpolation, convergence order

中图分类号:

O174.42

张淑婷, 王淑云, 何甲兴. 二元组合型三角插值多项式的收敛阶[J]. 吉林大学学报(工学版), 2002, (1): 52-56.

ZHANG Shu-ting, WANG Shu-yun, HE Jia-xing. Convergence Order of Double Variate Combination Trigonometric Interpolation Polynomials[J]. 吉林大学学报(工学版), 2002, (1): 52-56.

参考文献

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[5] He jiaxing. In reply to the question of S. N. Bernstein by trigonometric interpolation polynomial Indian［J］. J. Pare Appl. Math. 1996,27(6) :581～587.

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