A Matlab solver for the symplectic eigenvalue problem via trace minimization and Riemannian optimization
This solver aims to compute the symplectic eigenvalues and eigenvectors of a positive-definite matrix M. The major step is Riemannian optimization over the symplectic Stiefel manifold,
min trace(X'MX), s.t. X' J2n X = J2p,
where X is a 2n-by-2p matrix, J2n = [0 In; -In 0], and In is the n-by-n identity matrix.
Please run the demo test_cookup.m
Bin Gao, Nguyen Thanh Son, P.-A. Absil, Tatjana Stykel
- Riemannian optimization on the symplectic Stiefel manifold
- Symplectic eigenvalue problem via trace minimization and Riemannian optimization
- Nguyen Thanh Son (Thai Nguyen University of Sciences, Vietnam)
- Bin Gao (UCLouvain, Belgium)
Copyright (C) 2020, Nguyen Thanh Son, P.-A. Absil, Bin Gao, Tatjana Stykel
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/