• DOI:10.1007/978-3-030-80209-7_85
• Corpus ID: 232076233

Geometry of the Symplectic Stiefel Manifold Endowed with the Euclidean Metric

@inproceedings{Gao2021GeometryOT,
  title={Geometry of the Symplectic Stiefel Manifold Endowed with the Euclidean Metric},
  author={Bin Gao and Nguyen Thanh Son and Pierre-Antoine Absil and Tatjana Stykel},
  booktitle={GSI},
  year={2021}
}

• Bin Gao, N. T. Son, +1 author T. Stykel
• Published in GSI 28 February 2021
• Mathematics

The symplectic Stiefel manifold, denoted by Sp(2p, 2n), is the set of linear symplectic maps between the standard symplectic spaces R and R. When p = n, it reduces to the well-known set of 2n × 2n symplectic matrices. We study the Riemannian geometry of this manifold viewed as a Riemannian submanifold of the Euclidean space R. The corresponding normal space and projections onto the tangent and normal spaces are investigated. Moreover, we consider optimization problems on the symplectic Stiefel manifold. We obtain the expression of the Riemannian gradient with respect to the Euclidean metric, which then used in optimization algorithms. Numerical experiments on the nearest symplectic matrix problem and the symplectic eigenvalue problem illustrate the effectiveness of Euclidean-based algorithms.