Geodesic
Bounds of the matrix eigenvalues and its exponential by Lyapunov equation
Kybernetika, Tome 48 (2012) no. 5, pp. 865-878

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We are concerned with bounds of the matrix eigenvalues and its exponential. Combining the Lyapunov equation with the weighted logarithmic matrix norm technique, four sequences are presented to locate eigenvalues of a matrix. Based on the relations between the real parts of the eigenvalues and the weighted logarithmic matrix norms, we derive both lower and upper bounds of the matrix exponential, which complement and improve the existing results in the literature. Some numerical examples are also given.
Classification : 15A18, 15A60, 34D20
Keywords: Lyapunov equation; weighted logarithmic matrix norm; location of eigenvalues; bounds of the matrix exponential 
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     author = {Hu, Guang-Da and Mitsui, Taketomo},
     title = {Bounds of the matrix eigenvalues and its exponential by {Lyapunov} equation},
     journal = {Kybernetika},
     pages = {865--878},
     publisher = {mathdoc},
     volume = {48},
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     year = {2012},
     mrnumber = {3086856},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_5_a2/}
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Hu, Guang-Da; Mitsui, Taketomo. Bounds of the matrix eigenvalues and its exponential by Lyapunov equation. Kybernetika, Tome 48 (2012) no. 5, pp. 865-878. http://geodesic.mathdoc.fr/item/KYB_2012__48_5_a2/