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pro vyhledávání: '"Grudsky, S."'
We study the individual behavior of the eigenvalues of the laplacian matrices of the cyclic graph of order $n$, where one edge has weight $\alpha\in\mathbb{C}$, with $\operatorname{Re}(\alpha)<0$, and all the others have weights $1$. This paper is a
Externí odkaz:
http://arxiv.org/abs/2308.07514
The present work is devoted to the eigenvalue asymptotic expansion of the Toeplitz matrix $T_{n}(a)$ whose generating function $a$ is complex valued and has a power singularity at one point. As a consequence, $T_{n}(a)$ is non-Hermitian and we know t
Externí odkaz:
http://arxiv.org/abs/2211.15506
The analysis of the spectral features of a Toeplitz matrix-sequence $\left\{T_{n}(f)\right\}_{n\in\mathbb N}$, generated by a symbol $f\in L^1([-\pi,\pi])$, real-valued almost everywhere (a.e.), has been provided in great detail in the last century,
Externí odkaz:
http://arxiv.org/abs/2112.02685
Fine spectral estimates with applications to the optimally fast solution of large FDE linear systems
In the present note we consider a type of matrices stemming in the context of the numerical approximation of distributed order fractional differential equations (FDEs): from one side they could look standard, since they are, real, symmetric and posit
Externí odkaz:
http://arxiv.org/abs/2112.02681
We find uniform asymptotic formulas for all the eigenvalues of certain 7-diagonal symmetric Toeplitz matrices of large dimension. The entries of the matrices are real and we consider the case where the real-valued generating function such that its fi
Externí odkaz:
http://arxiv.org/abs/2111.07196
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Autor:
Batalshchikov, A. A., Grudsky, S. M., Malisheva, I. S., Mihalkovich, S. S., de Arellano, E. Ramirez, Stukopin, V. A.
This paper is devoted to the asymptotic behavior of all eigenvalues of Symmetric (in general non Hermitian) Toeplitz matrices with moderately smooth symbols which trace out a simple loop on the complex plane line as the dimension of the matrices incr
Externí odkaz:
http://arxiv.org/abs/1903.10551
Autor:
Böttcher, A., Grudsky, S. M.
This paper is devoted to asymptotic estimates for the condition numbers $\kappa(T_n(a))=||T_n(a)|| ||T_n^(-1)(a)||$ of large $n\cross n$ Toeplitz matrices $T_N(a)$ in the case where $\alpha \element L^\infinity$ and $Re \alpha \ge 0$. We describe sev
Akademický článek
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Publikováno v:
Journal of Mathematical Sciences; Apr2023, Vol. 271 Issue 2, p176-196, 21p