Abstract In this paper, we are concerned with the inversion of circulant matrices and their quantized tensor‐train (QTT) structure. particular, show that inverse a complex matrix , generated by first column form admits QTT representation ranks bounded . Under certain assumptions on entries also derive an explicit The latter can be used, for instance, to overcome stability issues arising when numerically solving differential equations periodic boundary conditions in format.

Abstract The paper describes a new open access computing resource nfusion.cs.msu.ru. includes modules for calculating equilibrium, vertical stability, plasma evolution, simulation systems magnetic diagnostics, as well algorithm constructing three-dimensional tetrahedral meshes in areas of complex structure. are integrated into unified software environment designed numerical support experiments on tokamak installations. possibility accessing the calculation server via Internet, data exchange...

Abstract The paper describes a new system of integrated modelling SIEMNED (Software and Information Environment for Modelling Numerical support Experiments on complex Devices) designed numerical experiments tokamak installations. Also discussed are the results its application to discharge scenarios at T-15 MD installation, which is currently being prepared physical launch.

Abstract The operation of modern tokamaks is impossible without an effective system for controlling the plasma boundary during discharge. In this paper, we consider a method determining on basis integral equations. A high-speed parallel code using GPUs was developed purpose. Different methods parallelization algorithm have been considered. possibility processing magnetic measurements in real time experiments shown. effect technical parameters (the number cores, data bus width, amount...

Abstract We study matrices over quotient rings modulo univariate polynomials a two-element field. Lower bounds for the fraction of invertible among all such given size are obtained. An efficient algorithm calculating determinant these and an generating random (with uniform distribution on set matrices) proposed analyzed. effective version latter form x r − 1 is considered These methods may find practical applications keys cryptographic schemes based quasi-cyclic codes as LEDAcrypt.

Article Invertible matrices over some quotient rings: identification, generation, and analysis was published on December 1, 2022 in the journal Discrete Mathematics Applications (volume 32, issue 6).

In this paper, we are concerned with the inversion of circulant matrices and their quantized tensor-train (QTT) structure. particular, show that inverse a complex matrix $A$, generated by first column form $(a_0,\dots,a_{m-1},0,\dots,0,a_{-n},\dots, a_{-1})^\top$ admits QTT representation ranks bounded $(m+n)$. Under certain assumptions on entries also derive an explicit $A^{-1}$. The latter can be used, for instance, to overcome stability issues arising when numerically solving differential...

Исследуются матрицы над факторкольцами кольца многочленов от одной переменной полем из двух элементов. Найдены нижние оценки доли обратимых матриц среди всех таких заданного размера. Предложен и проанализирован эффективный алгоритм вычисления определителя указанными факторкольцами, а также построения случайных (с равномерным распределением на множестве матриц). Рассмотрен вариант последнего алгоритма для факторколец по модулю вида $x^r - 1$. Эти алгоритмы могут найти практическое применение...