Exponentials of skew-symmetric matrices and logarithms of orthogonal matrices

Authors:
João R. Cardoso;F. Silva Leite
Affiliations:
Institute of Engineering of Coimbra, Rua Pedro Nunes, 3030-199 Coimbra, Portugal and Institute of Systems and Robotics, University of Coimbra, Pólo II, 3030-290 Coimbra, Portugal;Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal and Institute of Systems and Robotics, University of Coimbra, Pólo II, 3030-290 Coimbra, Portugal
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

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.