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Efficient computation of the matrix exponential by generalized polar decompositions. (English) Zbl 1084.65040
This paper deals with the computation of the matrix exponential in a manner that is consistent with Lie group structure. The need for such a study comes from solving systems of differential equations evolving in Lie groups and in homogeneous manifolds. Combining generalized polar decomposition with similarity transformations, a new method is proposed. The new method is more efficient in many settings than some classical ones.

MSC:
65F30Other matrix algorithms
15A24Matrix equations and identities
34A26Geometric methods in differential equations