AUTHORS: Said Agoujil, Abdeslem Hafid Bentbib

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ABSTRACT: This paper presents a symplectic J-SVD like decomposition of 2n-by-2m rectangular real matrix based on symplectic reflectors. The idea for this approach was to use symplectic reflectors to first reduce the matrix to J-bidiagonal form and then transform it to a diagonal form by using sequence of symplectic similarity transformations. This was done in parallel with the Golub-Kahan-Reinsch method. This method allowed us to compute eigenvalues for the skew-Hamiltonian matrix AJA.

KEYWORDS: Singular value decomposition (SVD), Hamiltonian matrix, Skew-Hamiltonian matrix, Symplectic matrix, Symplectic reflector

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