Numerical Algorithms

, Volume 39, Issue 4, pp 437–462 | Cite as

On theoretical and numerical aspects of symplectic Gram–Schmidt-like algorithms



Gram–Schmidt-like orthogonalization process with respect to a given skew-symmetric scalar product is a key step in model reduction methods, structure-preserving, for large sparse Hamiltonian eigenvalue problem. Theoretical as well as numerical aspects of this step do not benefit of enough attention, compared to the one allowed to the classical Gram–Schmidt algorithm and its modified version. The aim of this paper is to revisit the symplectic Gram–Schmidt algorithms, to built some modified versions and to deal with their theoretical and numerical features.


skew-symmetric scalar product symplectic Gram–Schmidt algorithms modified versions symplectic geometry large sparse Hamiltonian eigenvalue problem 


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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Pures et AppliquéesUniversité du Littoral–Côte d’OpaleCalais CedexFrance

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