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pro vyhledávání: '"Son Nguyen, Thanh"'
Autor:
Van Tiep, Dinh, Son, Nguyen Thanh
We consider the optimization problem with a generally quadratic matrix constraint of the form $X^TAX = J$, where $A$ is a given nonsingular, symmetric $n\times n$ matrix and $J$ is a given $k\times k$ matrix, with $k\leq n$, satisfying $J^2 = I_k$. S
Externí odkaz:
http://arxiv.org/abs/2410.22068
Optimization under the symplecticity constraint is an approach for solving various problems in quantum physics and scientific computing. Building on the results that this optimization problem can be transformed into an unconstrained problem on the sy
Externí odkaz:
http://arxiv.org/abs/2406.14299
Numerous problems in optics, quantum physics, stability analysis, and control of dynamical systems can be brought to an optimization problem with matrix variable subjected to the symplecticity constraint. As this constraint nicely forms a so-called s
Externí odkaz:
http://arxiv.org/abs/2211.09481
Autor:
Son, Nguyen Thanh, Stykel, Tatjana
Publikováno v:
Electronic Journal of Linear Algebra, 38, 607-616, 2022
Symplectic eigenvalues are conventionally defined for symmetric positive-definite matrices via Williamson's diagonal form. Many properties of standard eigenvalues, including the trace minimization theorem, are extended to the case of symplectic eigen
Externí odkaz:
http://arxiv.org/abs/2208.05291
Publikováno v:
In Computers and Geotechnics June 2024 170
Publikováno v:
Geometric Science of Information. GSI 2021. pp. 789--796
The symplectic Stiefel manifold, denoted by $\mathrm{Sp}(2p,2n)$, is the set of linear symplectic maps between the standard symplectic spaces $\mathbb{R}^{2p}$ and $\mathbb{R}^{2n}$. When $p=n$, it reduces to the well-known set of $2n\times 2n$ sympl
Externí odkaz:
http://arxiv.org/abs/2103.00459
Publikováno v:
In Linear Algebra and Its Applications 1 February 2024 682:50-85
Publikováno v:
SIAM Journal on Matrix Analysis and Applications, 42-4 (2021), 1732-1757
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 theorem. It is formulated as minimizing a trace cost function over the sym
Externí odkaz:
http://arxiv.org/abs/2101.02618
Autor:
Son, Nguyen Thanh, Van Tan, Tran
We establish a type of the Picard's theorem for entire curves in $P^n(\mathbb C)$ whose spherical derivative vanishes on the inverse images of hypersurface targets. Then, as a corollary, we prove that there is an union $D$ of finite number of hypersu
Externí odkaz:
http://arxiv.org/abs/2009.05259
Publikováno v:
SIAM Journal on Optimization, 31-2 (2021), 1546-1575
The symplectic Stiefel manifold, denoted by $\mathrm{Sp}(2p,2n)$, is the set of linear symplectic maps between the standard symplectic spaces $\mathbb{R}^{2p}$ and $\mathbb{R}^{2n}$. When $p=n$, it reduces to the well-known set of $2n\times 2n$ sympl
Externí odkaz:
http://arxiv.org/abs/2006.15226