| Abstract: |
| It is well known that matrix pseudospectrum is an important tool in the analysis of dynamical systems. However, the pseudospectral analysis is numerically quite costly for large-scale matrices. One possible direction of size-reduction could be to make use of the block structure of a matrix stemming from a variety of practical applications (discretization of partial differential equations etc.) and analyze the impact of the off-diagonal blocks on matrix pseudospectrum, in order to reduce computational costs while still obtaining useful approximations. In that sense, it is known that for a fixed perturbation size, the union of pseudospectra of diagonal blocks underestimates the pseudospetrum of a full matrix. So, one is interested to provide an upper estimate by adequately changing the size of the perturbation for the pseudospectra of diagonal blocks. For the case of a 2-by-2 block triangular matrix, this was optimally done by L. Grammont and A. Largillier. Here we extend this result to general block matrices and obtain some estimates for the distance to instability of a block matrix and present results applicable in the context of dynamical analysis of large-scale complex systems in the multidisciplinary ambiance including physics, ecology, medicine, chemistry, engineering, economy and many more. |
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