The central approximation theorems for the method of left gamma quasi-interpolants in <i>L_p</i> spaces

作     者：Müller, MW 

作者机构：Univ Dortmund Inst Angew Math Lehrstuhl Approximat Theorie VIII D-44221 Dortmund Germany 

出 版 物：《JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS》 (计算分析与应用杂志)

年 卷 期：2001年第3卷第3期

页      面：207-222页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：quasi-interpolants direct and inverse theorems left Gamma quasi-interpolant Gammaoperators in L-p spaces 

摘      要：The optimal degree of approximation of the method of Gammaoperators G(n) in L-p spaces is O(n(-1)). In order to obtain much faster convergence, quasi-interpolants G(n)((k)) of G(n) in the sense of Sablonniere are considered. We show that for fixed k the operator-norms \\G(n)((k))\\(p) are uniformly bounded in n. In addition to this, for the first time in the theory of quasi-interpolants, all central problems for approximation methods (direct theorem, inverse theorem, equivalence theorem) could be solved completely for the L-P metric. Left Gamma quasi-interpolants turn out to be as powerful as linear combinations of Garrunaoperators [6].