Subdivision Schemes for Positive Definite Matrices

被引：8
|
作者：
Itai, Uri [1 ]
Sharon, Nir [2 ]
机构：
[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel
[2] Tel Aviv Univ, Dept Math, IL-69978 Tel Aviv, Israel
来源：
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS | 2013年 / 13卷 / 03期
关键词：
Nonlinear subdivision scheme; Interpolation; Positive definite matrix; NONLINEAR SUBDIVISION; STRAIN;
D O I：
10.1007/s10208-012-9131-y
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
The class of symmetric positive definite matrices is an important class both in theory and application. Although this class is well studied, little is known about how to efficiently interpolate such data within the class. We extend the 4-point interpolatory subdivision scheme, as a method of interpolation, to data consisting of symmetric positive definite matrices. This extension is based on an explicit formula for calculating a binary "geodetic average". Our method generates a smooth curve of matrices, which retain many important properties of the interpolated matrices. Furthermore, the scheme is robust and easy to implement.
引用
收藏
页码：347 / 369
页数：23
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