Symplectic gram-schmidt algorithm with re-orthogonalization

Abstract EN

The preservation of symplectic Gram Schmidt Jorthogonality is crucial for structure preserving methods for the eigenvalue problem.

In this paper, we present the symplectic Gram Schmidt algorithm with re-orthogonalization and we study the recapture of the J-orthogonality of vectors generated by the algorithm.

Furthermore, the re-orthogonalization process is combined with a careful choice of the free parameters that was involved in the algorithm to ensure satisfactory re-capture of the J-orthogonality.

Some numerical experiments and computational aspects are given to confirm the superiority of the algorithm.