Publication
The distance to instability of a matrix A is a robust measure for the stability of the corresponding dynamical system x = Ax, known to be far more reliable than checking the eigenvalues of A. In this paper, a new algorithm for computing such a distance is sketched. Built on existing approaches, its computationally most expensive part involves a usually modest number of shift-and-invert Amoldi iterations. This makes it possible to address large sparse matrices, such as those arising from discretized partial differential equations.
Alfio Quarteroni, Francesco Regazzoni, Stefano Pagani
Aude Billard, Nadia Barbara Figueroa Fernandez, Mikhail Koptev