A fast algorithm for index of annihilation computations

In this paper a fast algorithm for computing the index of annihilation of the associated pencil of a given matrix is presented. Knowledge of this index leads us to the specification of the elementary divisors of the matrix and thus we can specify its canonical forms. It is shown that the new algorithm (which is based on the RRQR decomposition) is faster than the existing SVD approach. The algorithm can be also applied to matrix pencils and thus specify the structure of their elementary divisors.