Extremal functional -interpolation on an arbitrary mesh on the real axis. (1st April 2022)

• Record Type: Journal Article
• Authors: Subbotin, Yu. N.; Shevaldin, V. T.
• Is Part Of: Sbornik. Volume 213:Number 4(2022)
• Page Start: 556
• Page End: 577
• Publication Date: 2022-04-01
• Subjects: 41A05; 41A15 -- 41A50 -- 65D07; extremal interpolation -- derivative -- divided difference -- spline -- difference equation; Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM9628
• Languages: English
• ISSNs: 1064-5616

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.