计算机工程与应用 ›› 2010, Vol. 46 ›› Issue (1): 1-3.DOI: 10.3778/j.issn.1002-8331.2010.01.001

• 博士论坛 • 上一篇    下一篇

某型拟插值的多项式再生性

陈荣华1,韩旭里2,吴宗敏3   

  1. 1.湖南科技大学 数学与计算科学学院,湖南 湘潭 411201
    2.中南大学 数学科学与计算技术学院,长沙 410083
    3.复旦大学 数学科学学院,上海 200433
  • 收稿日期:2009-10-15 修回日期:2009-11-15 出版日期:2010-01-01 发布日期:2010-01-01
  • 通讯作者: 陈荣华

Property of polynomial reproducing for quasi-interpolation

CHEN Rong-hua1,HAN Xu-li2,WU Zong-min3   

  1. 1.School of Mathematics and Computational Science,Hunan University of Science and Technology,Xiangtan,Hunan 411201,China
    2.School of Mathematical Science and Computing Technology,Central South University,Changsha 410083,China
    3.School of Mathematical Science,Fudan University,Shanghai 200433,China
  • Received:2009-10-15 Revised:2009-11-15 Online:2010-01-01 Published:2010-01-01
  • Contact: CHEN Rong-hua

摘要: 研究某种特定形式的拟插值满足多项式再生性的充分必要条件。给出了几个定理,分别描述了常数再生、线性再生、二次多项式再生乃至一般的k次多项式再生的充分必要条件,并通过这些定理推出:LA不是常数再生的;LB是常数再生的但不是线性再生的;LD是线性再生的但不是二次多项式再生的。

关键词: 拟插值, 多项式再生, 常数再生, 线性再生

Abstract: In this paper,the sufficient and necessary conditions are studied for a sort of quasi-interpolation when it is polynomial reproducing.Some theorems are given which describe the sufficient and necessary conditions as the quasi-interpolation is constant reproducing,linear reproducing,quadratic polynomial reproducing and the general polynomial reproducing of degree k respectively.From these theorems,LA isn’t constant reproducing,LB is constant reproducing but not linear reproducing,and LD is linear reproducing but not quadratic polynomial reproducing.

Key words: quasi-interpolation, polynomial reproducing, constant reproducing, linear reproducing

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