Author:
Subbotin Yu. N.,Shevaldin V. T.
Abstract
Abstract
The Golomb-de Boor problem of extremal interpolation of infinite real sequences with smallest
-norm of the
th derivative of the interpolant,
, on an arbitrary mesh on the real axis is studied under constraints on the norms of the corresponding divided differences. For this smallest norm, lower estimates are obtained for any
in terms of
-splines. For the second derivative, this quantity is estimated from below and above by constants depending on the parameter
.
Bibliography: 13 titles.
Funder
Ministry of Science and Higher Education of the Russian Federation
Subject
Algebra and Number Theory
Reference15 articles.
1. $H^{m,p}$-extensions by $H^{m,p}$-splines;Golomb;J. Approximation Theory,1972
2. How small can one make the derivatives of an interpolating function?;de Boor;J. Approximation Theory,1975
3. Sur l'interpolation;Favard;J. Math. Pures Appl. (9),1940
4. On the connection between finite differences and corresponding derivatives;Subbotin,1965
5. Functional interpolation in the mean with smallest $n$ derivative;Subbotin,1967
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献