计算物理 ›› 1988, Vol. 5 ›› Issue (2): 221-231.

• 论文 • 上一篇    下一篇

W22[a,b]空间中的最佳Hermite插值算子

吴勃英1, 崔明根1, 邓中兴2   

  1. 1. 哈尔滨工业大学;
    2. 哈尔滨科技大学
  • 收稿日期:1987-01-01 修回日期:1988-06-01 出版日期:1988-06-25 发布日期:1988-06-25
  • 基金资助:
    国家自然科学基金

OPTIMUM HERMITEAN LNTERPOLATION OPERATOR IN THE W22 SPACE

Wu Bo-ying1, Cui Ming-gen1, Deng Zhong-xing2   

  1. 1. Harbin Institute of Technology;
    2. Harbin Institute of Science and Technique
  • Received:1987-01-01 Revised:1988-06-01 Online:1988-06-25 Published:1988-06-25

摘要: 本文介绍具有再生核的函数Hilbere空间W22给出了W22空间再生核的有限表达式,利用它构造出最佳Hilbere插值逼近算子(H2nu)(x)的真体表达式,当节点系无限加密时,能够保证(H2nu)(x)一致收敛于u(x),(H2nu)(y)一致收敛于u'(x),且每增加一个节点,误差在Sobolev范数意义下单调下降。

Abstract: In this paper we investigated the function space W22 which has a regenerate nucleus. We obtained a finite expression of the regenerate nucleus and used it to construct a concrete expression of the optimum Hermitean interpolation operator. It was also proved that, as the density of the node system increases infinitely, (H2nu)(x) and (H2nu)'(x) uniformly converge to u(x) and u'(x), respectively, and the error decreases to zero monotonically, under the Sobolev norm.