2024-03-29T08:13:06Zhttps://repositori.uji.es/oai/requestoai:repositori.uji.es:10234/1256462023-12-21T11:19:51Zcom_10234_7037com_10234_9col_10234_8635
00925njm 22002777a 4500
dc
Arnal, A.
author
Casas, Fernando
author
2015-07-01
We propose a new constructive procedure to factorize the fundamental real matrix of a linear system of differential equations as the product of the exponentials of a symmetric and a skew-symmetric matrix. Both matrices are explicitly constructed as series whose terms are computed recursively. The procedure is shown to converge for sufficiently small times. In this way, explicit exponential representations for the factors in the analytic polar decomposition are found. An additional advantage of the algorithm proposed here is that, if the exact solution evolves in a certain Lie group, then it provides approximations that also belong to the same Lie group, thus preserving important qualitative properties.
0377-0427
http://hdl.handle.net/10234/125646
10.1016/j.cam.2014.03.003
Exponential factorization
Polar decomposition
Exponential polar factorization of the fundamental matrix of linear differential systems