Approximation by Local L-Splines That Are Exact on Subspaces of the Kernel of a Differential Operator

被引：4

作者：

Strelkova, E. V. ^{[1
]}

Shevaldin, V. T. ^{[1
]}

机构：

[1] Russian Acad Sci, Ural Branch, Inst Math & Mech, Ekaterinburg 620990, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2011年 / 273卷

基金：

俄罗斯基础研究基金会;

关键词：

approximation; local L-splines; differential operator;

D O I：

10.1134/S0081543811050142

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct local L-splines with uniform knots that preserve subsets from the kernel of a linear differential operator L of order r with constant real coefficients and pairwise distinct roots of the characteristic polynomial. Pointwise estimates are found for the error of approximation by the constructed L-splines on classes of functions defined by differential operators of orders smaller than r.

引用

页码：S133 / S141

页数：9

共 17 条

[1] Approximation by local L-splines that are exact on subspaces of the kernel of a differential operator
Strelkova, E. V.
Shevaldin, V. T.
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2010, 16 (04): : 272 - 280
[2] Approximation by local ℒ-splines that are exact on subspaces of the kernel of a differential operator
E. V. Strelkova
V. T. Shevaldin
Proceedings of the Steklov Institute of Mathematics, 2011, 273 : 133 - 141
[3] Local L-Splines Preserving the Differential Operator Kernel
Shevaldina, E. V.
NUMERICAL ANALYSIS AND APPLICATIONS, 2010, 3 (01) : 90 - 99
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Shevaldin V.T.
Proceedings of the Steklov Institute of Mathematics, 2006, 255 (Suppl 2) : S178 - S197
[5] THE PERIODIC ANALOG OF ROLLES THEOREM FOR DIFFERENTIAL-OPERATORS AND APPROXIMATION BY L-SPLINES
NOVIKOV, SI
MATHEMATICAL NOTES, 1994, 56 (3-4) : 1061 - 1068
[6] Approximation by third-order local L-splines with uniform nodes
Zhdanov, P. G.
Shevaldin, V. T.
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2010, 16 (04): : 156 - 165
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JIA, RQ
JOURNAL OF APPROXIMATION THEORY, 1981, 33 (02) : 96 - 110
[8] On Approximation of Smooth Functions by L-Splines at a Point
Khudaya, Zh. V.
JOURNAL OF AUTOMATION AND INFORMATION SCIENCES, 2008, 40 (07) : 73 - 80
[9] APPROXIMATION OF A CLASS OF DIFFERENTIABLE FUNCTIONS BY L-SPLINES
NOVIKOV, SI
MATHEMATICAL NOTES, 1983, 33 (3-4) : 200 - 208
[10] Sharp Lebesgue constants for interpolatory L-splines of a formally self-adjoint differential operator
Kim, V. A.
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2011, 17 (03): : 169 - 177

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