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math.OC2021★ 39 cited
A Riemannian rank-adaptive method for low-rank matrix completion
Bin Gao, P. -A. Absil
The low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, a drawback of the known approaches is that the rank parameter has…
math.OC2021★ 3 cited
Geometry of the symplectic Stiefel manifold endowed with the Euclidean metric
Bin Gao, Nguyen Thanh Son, P. -A. Absil +1
The symplectic Stiefel manifold, denoted by , is the set of linear symplectic maps between the standard symplectic spaces and $\mathbb{R}^{2n}…
math.OC2021★ 20 cited
Symplectic eigenvalue problem via trace minimization and Riemannian optimization
Nguyen Thanh Son, P. -A. Absil, Bin Gao +1
We address the problem of computing the smallest symplectic eigenvalues and the corresponding eigenvectors of symmetric positive-definite matrices in the sense of Williamson's theo…