Symplectic Subspace Iteration Method for the J-SV D Decomposition

In [13] and [14], Xu presented an SV D-like decomposition to compute eigenvalues of JA T A and AJA T without explicit matrix-matrix products JA T A and AJA T .In this paper, we propose a method based on structured subspace iteration to compute the decomposition of a 2n-by-2m rectangular real matrix A, which we call the J-SV D method.Decompositions such as this one are intended to determine eigenvalues of skew-Hamiltonian matrix A J A = J T A T JA without having to calculate the product of these matrices.In this study, an algorithm based on a symplectic iterative subspace method is presented for computing the largest magnitude eigenvalues of skew-Hamiltonian matrices, and its convergence theory is discussed.