Interpolatory pointwise estimates for polynomial approximation

被引：15
|
作者：
Gonska, HH [1 ]
Leviatan, D
Shevchuk, IA
Wenz, HJ
机构：
[1] Univ Duisburg, Fachbereich Math, D-47048 Duisburg, Germany
[2] Tel Aviv Univ, Sackler Fac Exact Sci, Sch Math Sci, IL-69978 Tel Aviv, Israel
来源：
CONSTRUCTIVE APPROXIMATION | 2000年 / 16卷 / 04期
关键词：
approximation by polynomials; shape-preserving approximation; degree of approximation; interpolatory pointwise estimates;
D O I：
10.1007/s003650010008
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We discuss whether or not it is possible to have interpolatory pointwise estimates in the approximation of a function f is an element of C[0, 1], by polynomials. For the sake of completeness, as well as in order to strengthen some existing results, we discuss briefly the situation in unconstrained approximation. Then we deal with positive and monotone constraints where we show exactly when such interpolatory estimates are achievable by proving affirmative results and by providing the necessary counterexamples in all other cases.
引用
收藏
页码：603 / 629
页数：27
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