Abstract
The Lanczos algorithm is a well known procedure to compute few eigenvalues of large symmetric matrices. We slightly modify this algorithm in order to obtain the eigenvalues of Hamiltonian matrices H = JS with S symmetric and positive definite. These matrices represent a significant subclass of Hamiltonian matrices since their eigenvalues lie on the imaginary axis. An implicitly restarted procedure is also considered in order to speed-up the convergence of the algorithm.
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