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Symplectic Modified Gram-Schmidt as A Symplectic Householder SR Factorization

S. Agoujil, A. H. bentbib


Symplectic SR factorization play a key role in solving the continuous-time algebraic Riccati equation and specially problem of computing the eigenvalues of Hamiltonian matrices. The goal of this paper is to describe an essential role of symplectic complex transformation based on symplectic Householder transformation in SR factorization. We treat proof which shows that a Symplectic Modified Gram-Schmidt process applied to a 2m-by-2n complex matrix can be interpreted as a Symplectic Householder SR factorization of the augmented matrix. Some numerical experiments are given.


SR factorization, Symplectic Householder, Symplectic Modified Gram-Schmidt.

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