On specific stability bounds for linear multiresolution schemes based on piecewise polynomial Lagrange interpolation

被引：7

作者：

Amat, Sergio ^{[1
]}

Donat, Rosa ^{[2
]}

Carlos Trillo, J. ^{[1
]}

机构：

[1] Univ Politecn Cartagena, Dept Matemat Aplicada & Estadist, Cartagena, Spain

[2] Univ Valencia, Dept Matemat Aplicada, E-46003 Valencia, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 358卷 / 01期

关键词：

Stability; Linear multiresolution; Piecewise Lagrange interpolation;

D O I：

10.1016/j.jmaa.2009.04.038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Deslauriers-Dubuc symmetric interpolation process can be considered as an interpolatory prediction scheme within Harten's framework. In this paper we express the Deslauriers-Dubuc prediction operator as a combination of either second order or first order differences. Through a detailed analysis of certain contractivity properties, we arrive to specific l(infinity)-stability bounds for the multiresolution transform. A variety of tests indicate that these l(infinity) bounds are closer to numerical estimates than those obtained with other approaches. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：18 / 27

页数：10

共 50 条

[1] Optimal bounds for a Lagrange interpolation inequality for piecewise linear continuous finite elements in two space dimensions
Muhamadiev, Ergash
Nazarov, Murtazo
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 423 (02) : 940 - 955
[2] THE NUMERICAL STABILITY OF EVALUATION SCHEMES FOR POLYNOMIALS BASED ON THE LAGRANGE INTERPOLATION FORM
RACK, HJ
REIMER, M
[J]. BIT, 1982, 22 (01): : 101 - 107
[3] Using Piecewise Hashing and Lagrange Interpolation Polynomial to Preserve Electronic Evidence
Song, Xiuli
Deng, Hongyao
Xiong, Zhihai
[J]. ADVANCES IN INFORMATION TECHNOLOGY AND EDUCATION, PT I, 2011, 201 : 472 - +
[4] LAGRANGE INTERPOLATION SET ALONG LINEAR PIECEWISE ALGEBRAIC CURVES
Wang, Ren-Hong
Wang, Shao-Fan
[J]. COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2009, 7 (01) : 165 - 174
[5] Sharp error bounds for piecewise linear interpolation of planar curves
Degen, W. L. F.
[J]. COMPUTING, 2007, 79 (2-4) : 143 - 151
[6] Sharp error bounds for piecewise linear interpolation of planar curves
W. L. F. Degen
[J]. Computing, 2007, 79 : 143 - 151
[7] Almost linear VC dimension bounds for piecewise polynomial networks
Bartlett, PL
Maiorov, V
Meir, R
[J]. ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 11, 1999, 11 : 190 - 196
[8] A Group Authentication Scheme based on Lagrange Interpolation Polynomial
Li, Shi
Doh, Inshil
Chae, Kijoon
[J]. 2016 10TH INTERNATIONAL CONFERENCE ON INNOVATIVE MOBILE AND INTERNET SERVICES IN UBIQUITOUS COMPUTING (IMIS), 2016, : 386 - 391
[9] Precise integration methods based on Lagrange piecewise interpolation polynomials
Wang, Meng-Fu
Au, F. T. K.
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2009, 77 (07) : 998 - 1014
[10] Almost linear VC-dimension bounds for piecewise polynomial networks
Bartlett, PL
Maiorov, V
[J]. NEURAL COMPUTATION, 1998, 10 (08) : 2159 - 2173

← 1 2 3 4 5 →