Kybernetika 48 no. 5, 865-878, 2012

Bounds of the matrix eigenvalues and its exponential by Lyapunov equation

Guang-Da Hu and Taketomo Mitsui

Abstract:

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.

Keywords:

Lyapunov equation, weighted logarithmic matrix norm, location of eigenvalues, bounds of the matrix exponential

Classification:

15A18, 15A60, 34D20

paper.pdf

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