On the stability of large matrices
The distance \(\text{rstab} (A)\) of a stable matrix \(A\) to the set of unstable matrices and the norm of the exponential of matrices constitute two important topics in stability theory. The method proposed partitions the matrix into two blocks; a small block in which the stability is studied and a large block whose field of values is located in the complex plane. Using the information on the blocks and some results on perturbation theory, the authors give sufficient conditions for the stability of the original matrix, a lower bound of \(\text{rstab}(A)\) and an upper bound on the norm of the exponential of \(A\). They illustrate these theoretical bounds on a practical test problem. The paper contains sections of introduction, on the stability of matrices, case of large matrices numerical experiments, and conclusion.
scientific article; zbMATH DE number 1331066
scientific article