Property of polynomial reproducing for quasi-interpolation

doi:10.3778/j.issn.1002-8331.2010.01.001

Computer Engineering and Applications ›› 2010, Vol. 46 ›› Issue (1): 1-3.DOI: 10.3778/j.issn.1002-8331.2010.01.001

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Property of polynomial reproducing for quasi-interpolation

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

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

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.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

通讯作者: 陈荣华

Abstract

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，L_A isn’t constant reproducing，L_B is constant reproducing but not linear reproducing，and L_D is linear reproducing but not quadratic polynomial reproducing.

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

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：L_A不是常数再生的；L_B是常数再生的但不是线性再生的；L_D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

CLC Number:

TP301.6

CHEN Rong-hua¹，HAN Xu-li²，WU Zong-min³. Property of polynomial reproducing for quasi-interpolation[J]. Computer Engineering and Applications, 2010, 46(1): 1-3.

陈荣华¹，韩旭里²，吴宗敏³. 某型拟插值的多项式再生性[J]. 计算机工程与应用, 2010, 46(1): 1-3.

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Property of polynomial reproducing for quasi-interpolation

某型拟插值的多项式再生性

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