Lagrange Interpolatory Subdivision Schemes in Chebyshev Spaces
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- 作者：Marie-Laurence Mazure
- 关键词：Subdivision ; Lagrange interpolatory schemes ; Non ; nested grids ; Extended Chebyshev spaces ; Chebyshevian divided differences ; Blossoms ; 41A05 ; 41A50 ; 65D05 ; 65D17
- 刊名：Foundations of Computational Mathematics
- 出版年：2015
- 出版时间：August 2015
- 年：2015
- 卷：15
- 期：4
- 页码：1035-1068
- 全文大小：768 KB
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1. Laboratoire Jean Kuntzmann, Universit茅 Joseph Fourier, BP53, 38041聽, Grenoble Cedex 9, France - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Numerical Analysis
Computer Science, general
Math Applications in Computer Science
Linear and Multilinear Algebras and Matrix Theory
Applications of Mathematics - 出版者：Springer New York
- ISSN：1615-3383
文摘
We develop an efficient approach to the analysis of Lagrange interpolatory subdivision schemes based on Extended Chebyshev spaces of any even dimension. In general, such schemes are non-uniform and non-stationary. The study confirms and extends some ideas concerning more generally the analysis of non-regular subdivision schemes already presented in earlier papers. One crucial step consists in finding (non-regular) grids naturally adapted to the initial scheme in view of defining its derived schemes, a change of grid being possibly necessary for each additional order of smoothness considered. Surprisingly, it may be the case that the natural grids are non-nested, even though the initial scheme is interpolatory. This is so in particular for Chebyshevian Lagrange interpolatory schemes, for which the natural grids are defined in terms of Chebyshevian divided differences. Comparison of the corresponding successive derived schemes with their polynomial counterparts enables us to show that they have similar behaviours.