Finding the distance to instability of a large sparse matrix

Kressner, Daniel2011-05-052011-05-052011-05-05200610.1109/CACSD-CCA-ISIC.2006.4776620https://infoscience.epfl.ch/handle/20.500.14299/67113The 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.Rightmost EigenvaluesStability RadiusInfinity-NormAlgorithmTransformationsComputationPencilsFinding the distance to instability of a large sparse matrixtext::conference output::conference proceedings::conference paper