On a nonlinear 4-point ternary and non-interpolatory subdivision scheme eliminating the Gibbs phenomenon

被引：4
|
作者：
Amat, S. [1 ]
Choutri, A. [2 ]
Ruiz, J. [3 ]
Zouaoui, S. [4 ]
机构：
[1] Univ Politecn Cartagena, Dept Matemat Aplicada & Estadist, Cartagena, Spain
[2] ENS Kouba, Dept Math, Algiers, Algeria
[3] Univ Alcala UAH, Dept Phys & Math, Alcala De Henares, Spain
[4] Ecole Preparatoire Sci & Tech Alger, Lab EDPNLHM ENS Kouba, Algiers, Algeria
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 320卷
关键词：
Nonlinear ternary non-interpolatory subdivision scheme; Regularity; Nonlinear subdivision; Stability; Gibbs phenomenon; Signal processing; MEDIAN-INTERPOLATION; MULTIRESOLUTION; CURVES;
D O I：
10.1016/j.amc.2017.08.055
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A nonlinear ternary 4-point non-interpolatory subdivision scheme is presented. It is based on a nonlinear perturbation of the 4-point subdivision scheme studied in [16]. The convergence of the scheme and the regularity of the limit function are analyzed. It is shown that the Gibbs phenomenon, that is classical in linear schemes, is eliminated. We also establish the stability of the subdivision scheme, that is not a consequence of its convergence due to its non-linearity. To the best of our knowledge, this is the first ternary non-interpolatory subdivision scheme that can be found in the literature. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：16 / 26
页数：11
相关论文
共 47 条
  • [1] ON A NONLINEAR 4-POINT TERNARY AND INTERPOLATORY MULTIRESOLUTION SCHEME ELIMINATING THE GIBBS PHENOMENON
    Amat, S.
    Dadourian, K.
    Liandrat, J.
    INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2010, 7 (02) : 261 - 280
  • [2] On a nonlinear 4-point quaternary approximating subdivision scheme eliminating the Gibbs phenomenon
    Amat S.
    Liandrat J.
    SeMA Journal, 2013, 62 (1): : 15 - 25
  • [3] Fractal behavior of ternary 4-point interpolatory subdivision scheme with tension parameter
    Siddiqi, Shahid S.
    Salam, Wardat Us
    Butt, Nadeem Ahmad
    APPLIED MATHEMATICS AND COMPUTATION, 2015, 260 : 148 - 158
  • [4] Generation of fractal curves and surfaces using ternary 4-point interpolatory subdivision scheme
    Siddiqi, Shahid S.
    Idrees, Usama
    Rehan, Kashif
    APPLIED MATHEMATICS AND COMPUTATION, 2014, 246 : 210 - 220
  • [5] A combined ternary 4-point subdivision scheme
    Rehan, Kashif
    Sabri, Muhammad Athar
    APPLIED MATHEMATICS AND COMPUTATION, 2016, 276 : 278 - 283
  • [6] A ternary 4-point approximating subdivision scheme
    Ko, Kwan Pyo
    Lee, Byung-Gook
    Yoon, Gang Joon
    APPLIED MATHEMATICS AND COMPUTATION, 2007, 190 (02) : 1563 - 1573
  • [7] Fairing geometric modeling based on 4-point interpolatory subdivision scheme
    Luo, XN
    Liu, N
    Gao, CY
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 163 (01) : 189 - 197
  • [8] Differentiability of a 4-point ternary subdivision scheme and its application
    Zheng, Hongchan
    Zhao, Hongxing
    Ye, Zhenglin
    Zhou, Min
    IMECS 2006: International Multiconference of Engineers and Computer Scientists, 2006, : 231 - 236
  • [9] A combined approximating and interpolating ternary 4-point subdivision scheme
    Zhang, Li
    Ma, Huanhuan
    Tang, Shuo
    Tan, Jieqing
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 349 : 563 - 578
  • [10] Shape Preservation of Ternary 4-point Non-Stationary Interpolating Subdivision Scheme
    Bibi, Khalida
    Akram, Ghazala
    Rehan, Kashif
    PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS, 2020, 52 (01): : 77 - 97
12345