Solving Hamiltonian systems arising from ODE eigenproblems

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Carsten R. Maple, Marco Marletta

Published: 1999, Last Modified: 12 Nov 2025Numer. Algorithms 1999EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: This paper presents an algorithm for solving a linear Hamiltonian system arising in the study of certain ODE eigenproblems. The method follows the phase angles of an associated unitary matrix, which are essential for correct indexing of the eigenvalues of the ODE. Compared to the netlib code SL11F [11] the new method has the property that on many important problems – in particular, on matrix–vector Schrödinger equations – the cost of the integration is bounded independently of the eigenparameter λ. This allows large eigenvalues to be found much more efficiently. Numerical results show that our implementation of the new algorithm is substantially faster than the netlib code SL11F.