An Algorithm for Computing the Distance to Instability

An algorithm is developed for computing the distance to instability of an n × n matrix. It is aimed primarily at sparse matrices and can be used for any value of n provided that an eigenvalue problem for a (2n) × (2n) Hamiltonian matrix can be solved on the computer being used. The algorithm gives both a lower bound and an upper bound for the distance in guaranteed accuracy. The method is faster than other currently available methods.

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