Exponentials of skew-symmetric matrices and logarithms of orthogonal matrices
Exponentials of skew-symmetric matrices and logarithms of orthogonal matrices
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DOI：
10.1016/j.cam.2009.11.032
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发表时间：
2010-04-01
影响因子：
2.4
通讯作者：
Leite, F. Silva
中科院分区：
文献类型：
--
作者：
Cardoso, Joao R.;Leite, F. Silva
两种广泛使用的计算矩阵指数和矩阵平方的方法分别是缩放平方法和逆缩放平方法。这两种方法与Pade近似相结合时都是有效的。本文讨论了反对称矩阵的指数和正交矩阵的幂的计算。我们的主要目标是通过利用反对称矩阵和正交矩阵的特殊结构来改进这两种方法。矩阵的指数和对数的几何特征和扩展的特殊欧几里德刚性运动组也得到了解决。(C)2009爱思唯尔有限公司版权所有。
Two widely used methods for computing matrix exponentials and matrix logarithms are, respectively, the scaling and squaring and the inverse scaling and squaring. Both methods become effective when combined with Pade approximation. This paper deals with the computation of exponentials of skew-symmetric matrices and logarithms of orthogonal matrices. Our main goal is to improve these two methods by exploiting the special structure of skew-symmetric and orthogonal matrices. Geometric features of the matrix exponential and logarithm and extensions to the special Euclidean group of rigid motions are also addressed. (C) 2009 Elsevier B.V. All rights reserved.