Error bounds for anisotropic RBF interpolation

被引：13

作者：

Beatson, Rick ^{[2
]}

Davydov, Oleg ^{[1
]}

Levesley, Jeremy ^{[3
]}

机构：

[1] Univ Strathclyde, Dept Math, Glasgow G1 1XH, Lanark, Scotland

[2] Univ Canterbury, Dept Math & Stat, Christchurch 1, New Zealand

[3] Univ Leicester, Dept Math, Leicester LE1 7RH, Leics, England

来源：

JOURNAL OF APPROXIMATION THEORY | 2010年 / 162卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Radial basis functions; Anisotropic approximation;

D O I：

10.1016/j.jat.2009.08.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present error bounds for the interpolation with anisotropically transformed radial basis functions for both a function and its partial derivatives. The bounds rely on a growth function and do not contain unknown constants. For polyharmonic basic functions in R-2, we show that the anisotropic estimates predict a significant improvement of the approximation error if both the target function and the placement of the centers are anisotropic, and this improvement is confirmed numerically. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：512 / 527

页数：16

共 50 条

[21] Best error bounds for deficient quartic spline interpolation
Rana, SS
Dubey, YP
[J]. INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 1999, 30 (04): : 385 - 393
[22] Best error bounds of deficient quintic spline interpolation
Rana, SS
Dubey, YP
[J]. INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 1997, 28 (10): : 1337 - 1344
[23] ON QUARTIC AND QUINTIC INTERPOLATION SPLINES AND THEIR OPTIMAL ERROR BOUNDS
王建忠
黄达人
[J]. Science China Mathematics, 1982, (11) : 1130 - 1141
[24] Upper Bounds for the Error in Some Interpolation and Extrapolation Designs
Broniatowski, Michel
Celant, Giorgio
Di Battista, Marco
Leoni-Aubin, Samuela
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2012, 41 (16-17) : 3002 - 3019
[25] BEST ERROR-BOUNDS FOR QUARTIC SPLINE INTERPOLATION
HOWELL, G
VARMA, AK
[J]. JOURNAL OF APPROXIMATION THEORY, 1989, 58 (01) : 58 - 67
[26] Interpolation error estimates for edge elements on anisotropic meshes
Lombardi, Ariel L.
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2011, 31 (04) : 1683 - 1712
[27] General theory of interpolation error estimates on anisotropic meshes
Hiroki Ishizaka
Kenta Kobayashi
Takuya Tsuchiya
[J]. Japan Journal of Industrial and Applied Mathematics, 2021, 38 : 163 - 191
[28] Anisotropic interpolation error estimates via orthogonal expansions
Li, Mingxia
Mao, Shipeng
[J]. CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2013, 11 (04): : 621 - 629
[29] General theory of interpolation error estimates on anisotropic meshes
Ishizaka, Hiroki
Kobayashi, Kenta
Tsuchiya, Takuya
[J]. JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2021, 38 (01) : 163 - 191
[30] Sharp error bounds for piecewise linear interpolation of planar curves
Degen, W. L. F.
[J]. COMPUTING, 2007, 79 (2-4) : 143 - 151

← 1 2 3 4 5 →