On divergence of Hermite-Fejer interpolation to f(z) = z in the complex plane

被引：5
|
作者：
Brutman, L [1 ]
Gopengauz, I
机构：
[1] Univ Haifa, Dept Comp Sci, IL-31905 Haifa, Israel
[2] Moscow Steel & Alloys Inst, Dept Math, Moscow 117936, Russia
来源：
CONSTRUCTIVE APPROXIMATION | 1999年 / 15卷 / 04期
关键词：
Hermite-Fejer interpolation; divergence;
D O I：
10.1007/s003659900124
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that for a broad class of interpolatory matrices on [-1, 1] the sequence of polynomials induced by Hermite-Fejer interpolation to f(z) = z diverges everywhere in the complex plane outside the interval of interpolation [-1, 1]. This result is in striking contrast to the behavior of the Lagrange interpolating polynomials.
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页码：611 / 617
页数：7
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