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pro vyhledávání: '"Stykel, Tatjana"'
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
Analysis of a quasilinear coupled magneto-quasistatic model: solvability and regularity of solutions
We consider a~quasilinear model arising from dynamical magnetization. This model is described by a~magneto-quasistatic (MQS) approximation of Maxwell's equations. Assuming that the medium consists of a~conducting and a~non-conducting part, the deriva
Externí odkaz:
http://arxiv.org/abs/2205.15727
Autor:
Reis, Timo, Stykel, Tatjana
We study a~quasilinear coupled magneto-quasistatic model from a~systems theoretic perspective.} First, by taking the injected voltages as input and the associated currents as output, we prove that the magneto-quasistatic system is passive. Moreover,
Externí odkaz:
http://arxiv.org/abs/2205.15259
This paper addresses the numerical solution of nonlinear eigenvector problems such as the Gross-Pitaevskii and Kohn-Sham equation arising in computational physics and chemistry. These problems characterize critical points of energy minimization probl
Externí odkaz:
http://arxiv.org/abs/2108.09831
Publikováno v:
In Linear Algebra and Its Applications 1 February 2024 682:50-85
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:
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
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