Symplectic Subspace Iteration Method for the J-SV D Decomposition

73384dd2-40e0-41ca-a001-865abdcb0c5120250811100612377wseas:wseasmdt@crossref.orgMDT DepositInternational Journal of Applied Mathematics, Computational Science and Systems Engineering2766-982310.37394/232026https://wseas.com/journals/amcse/31220253122025710.37394/232026.2025.7https://wseas.com/journals/amcse/2025.phpSymplectic Subspace Iteration Method for the J-SV D DecompositionAhmedKanberCRMEF Marrakesh, MOROCCOA. H.BentbibLaboratory LAMAI, University of Cadi Ayyad, Marrakesh, MOROCCO8112025811202518819616https://wseas.com/journals/amcse/2025/a32amcse-011(2025).pdf10.37394/232026.2025.7.16https://wseas.com/journals/amcse/2025/a32amcse-011(2025).pdfS. Agoujil and A. H. Bentbib. An Implicity Symplectic Lanczos Algorithm for Hamiltonian Matrices. International Journal Tomography and Simulation, Number F08, Volume 10, 2008. S. Agoujil and A. H. Bentbib. New symplectic transformation on C 2n×2 : Symplectic reflectors. Int. Jour. of Tomography and Statistics (IJTS), 11, pp. 99–117,Summer 2009. S. Agoujil, A. H. Bentbib and A. Kanber. A Structured SVD-Like Decomposition. Wseas Transactions on Mathematics, Issue 7, Volume 11, July 2012. 10.1007/s40314-016-0346-4S. Agoujil, A. H. Bentbib and A. Kanber. An iterative method for computing a symplectic SVD-like decomposition, Comp. Appl. Math. 37, 349–363 (2018). 10.1007/s40314-016-0346-4S. Agoujil, A. H. Bentbib and A. Kanber. Symplectic Golub-Kahan-Reinsch SVD-like matrix decomposition, J. Adv. Math. Stud. Vol. 11, No. 2, 203–213 (2018). A. H. Bentbib and A. Kanber. A method for solving Hamiltonian eigenvalue problem, Int. Jour. Math. Stat. (IJMS) 7 Winter(2010). M. Bassour and A. H. Bentbib. Factorization of RJR of skew-Hamiltonian matrix using its Hamiltonian square root. Int. Jour. of Tomography and Statistics (IJTS), 8 Springer 2011. P. Benner, R. Byer, H. Fassender, V. Merhrmann, D. Watkins. Cholesky-Like Factorizations of skew-Symmetric Matrices. Electronic Transactions on Numerical Analysis, Volume 11, pp. 85-93, 2000. 10.1007/1-4020-3197-1_1P. Benner, D. Kressner, V. Merhrmann. Skew-Hamiltonian an Hamiltonian eigenvalue problems: Theory, Algorithms and Applications Mathematics for key technologies? (FZT 86) 10.1137/0702016G. Golub, W. Kahan. Calculating the Singular Values and Pseudo-Inverse of Matrix. J. SIAM Numerical Analysis, Ser. B, Vol 2 N. 2 printed in U. S. A, pp. 205–224, 1965. 10.1007/978-3-662-39778-7_10G. Golub and C. Reinsch. Singular Value Decomposition and Least Square Solutions. In J. H. Wilkinson and C. Reinsch, editors, Linear Algebra, volume II of Handbook for Automatic Computations, chapter I/10, pages 134–151. Springer Verlag, 1971. 10.1016/0024-3795(84)90034-xC. Van Loan: A Symplectic method for approximating all the eigenvalues of Hamiltonian matrix, LAA. 61:233-251 (1984). 10.1016/s0024-3795(03)00370-7H. Xu. An SVD-like matrix decomposition and its applications, Linear Algebra and its Applications, 368, pp. 1–24, 2003. 10.1137/s0895479802410529H. Xu. A Numerical Method For computing An SVD-like matrix decomposition. SIAM journal on matrix analysis and applications, 26, pp. 1058–1082, 2005.