摘要
本文研究了基于第二类切比雪夫结点的二元拉格朗日插值多项式的勒贝格常数下界估计,证明其阶为n^(2),并得到此拉格朗日插值多项式L_(n)(f)不能对[-1,1]×[-1,1]上所有连续函数f(x,y)一致收敛.
The lower bound of the Lebesgue constant of the bivariate Lagrange interpolation polynomial based on the second kind of Chebyshev polynomial is studied in this paper,and its order is proved to be n^(2).Further,it follows that this Lagrange interpolation polynomial L_(n)(f)does not uniformly converge for all continuous functions f(x,y)on[-1,1]×[-1,1].
作者
刘娟
朱来义
LIU Juan;ZHU Laiyi(School of Mathematics and Physics,Handan University,Handan,Hebei,056005,P.R.China;School of Mathematics,Renmin University of China,Beijing,100872,P.R.China)
出处
《数学进展》
CSCD
北大核心
2023年第3期497-510,共14页
Advances in Mathematics（China）
基金
国家自然科学基金(No.11571362)
河北省自然科学基金(No.A2019109076)
邯郸市科学技术研究与发展计划项目(No.1523103064-6)
邯郸学院光谱科技创新团队项目(No.XKYTD202002)
