International Journal of Applied Mathematics, Computational Science and Systems Engineering
E-ISSN: 2766-9823
Volume 7, 2025
Symplectic Subspace Iteration Method for the J-SV D Decomposition
Authors: ,
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Abstract: 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.
Pages: 188-196
DOI: 10.37394/232026.2025.7.16