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Найдено 7 публикаций
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Статья
Remizov I. Applied Mathematics and Computation. 2018. Vol. 328. P. 243-246.
Добавлено: 25 мая 2018
Статья
Nesterov Y., Nemirovski A. Applied Mathematics and Computation. 2014.
Добавлено: 28 января 2016
Статья
Shapoval A., Le Mouël J., Courtillot V. et al. Applied Mathematics and Computation. 2020. Vol. 386. P. 125485.
Добавлено: 22 июля 2020
Статья
Protasov V. Y., Guglielmi N., Conti C. et al. Applied Mathematics and Computation. 2016. Vol. 272. No. 1. P. 20-27.
Добавлено: 20 февраля 2016
Статья
Ducomet Bernard, Zlotnik Alexander, Romanova Alla. Applied Mathematics and Computation. 2015. Vol. 255. P. 195-206.

An initial-boundary value problem for the n  -dimensional ($n\geq 2$) time-dependent Schrödinger equation in a semi-infinite parallelepiped is considered. Starting from the Numerov–Crank–Nicolson finite-difference scheme, we first construct higher order scheme with splitting space averages having much better spectral properties for $n\geq 3$. Next we apply the Strang-type splitting with respect to the potential and, third, construct discrete transparent boundary conditions (TBC). For the resulting double-splitting method, the uniqueness of solution and the uniform in time L2-stability are proved and an error estimate is stated. Owing to the splitting, an effective direct algorithm using FFT (in the coordinate directions perpendicular to the leading axis of the parallelepiped) is applied to implement the scheme for general potential.

Добавлено: 10 октября 2014
Статья
Sinelshchikov D., Кудряшов Н. А. Applied Mathematics and Computation. 2017. Vol. 307. P. 257-264.
Добавлено: 11 февраля 2019
Статья
Chebotarev A., Teretenkov A. E. Applied Mathematics and Computation. 2014. Vol. 234. P. 380-384.

We describe a simple implementation of the Takagi factorization of symmetric matrices $A = U\Lambda U^T$ with unitary $U$ and diagonal $\Lambda$ in terms of the square root of an auxiliary unitary matrix and the singular value decomposition of $A$. The method is based on an algebraically exact expression. For parameterized family $A_\epsilon = A +\epsilon R = U_\epsilon \Lambda_\epsilon U^T_\epsilon$, $\epsilon >0$ with distinct singular values, the unitary matrices $U_\epsilon$ are discontinuous at the point $\epsilon = 0$, if the singular values of $A$ are multiple, but the composition $U_\epsilon \Lambda_\epsilon U^T_\epsilon$ remains numerically stable and converges to $A$. The factorization is represented as a fast and compact algorithm. Its demo version for Wolfram Mathematica and interactive numerical tests are available on Internet.

Добавлено: 4 июня 2014