Zobrazeno 1 - 10
of 27
pro vyhledávání: '"Savostyanov, Dmitry V."'
Publikováno v:
Applied Mathematics and Computation 460:128290, 2024
To improve mathematical models of epidemics it is essential to move beyond the traditional assumption of homogeneous well--mixed population and involve more precise information on the network of contacts and transport links by which a stochastic proc
Externí odkaz:
http://arxiv.org/abs/2209.03756
Publikováno v:
Numerical Mathematics and Advanced Applications - ENUMATH 2013, in Lecture Notes in Computational Science and Engineering. 103:335-343, 2015
Given in the title are two algorithms to compute the extreme eigenstate of a high-dimensional Hermitian matrix using the tensor train (TT) / matrix product states (MPS) representation. Both methods empower the traditional alternating direction scheme
Externí odkaz:
http://arxiv.org/abs/1312.6542
Publikováno v:
Computer Physics Communications 185(4):1207-1216, 2014
We consider an approximate computation of several minimal eigenpairs of large Hermitian matrices which come from high--dimensional problems. We use the tensor train format (TT) for vectors and matrices to overcome the curse of dimensionality and make
Externí odkaz:
http://arxiv.org/abs/1306.2269
Autor:
Savostyanov, Dmitry V.
Publikováno v:
Linear Algebra and its Applications 458:217-244 (2014)
We consider a cross interpolation of high-dimensional arrays in the tensor train format. We prove that the maximum-volume choice of the interpolation sets provides the quasioptimal interpolation accuracy, that differs from the best possible accuracy
Externí odkaz:
http://arxiv.org/abs/1305.1818
Publikováno v:
SIAM J. Sci. Comput. 36(5): A2248-A2271, 2014
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization of the ene
Externí odkaz:
http://arxiv.org/abs/1304.1222
Publikováno v:
Journal of Computational and Applied Mathematics 260:434-448, 2014
We address a linear fractional differential equation and develop effective solution methods using algorithms for inversion of triangular Toeplitz matrices and the recently proposed QTT format. The inverses of such matrices can be computed by the divi
Externí odkaz:
http://arxiv.org/abs/1211.5384
Publikováno v:
In Applied Mathematics and Computation 15 January 2016 273:604-623
Autor:
Savostyanov, Dmitry V.
Publikováno v:
In Linear Algebra and Its Applications 1 October 2014 458:217-244
Autor:
Savostyanov, Dmitry V.1 dmitry.savostyanov@gmail.com
Publikováno v:
Numerical Mathematics: Theory, Methods & Applications. Nov2009, Vol. 2 Issue 4, p439-444. 6p. 1 Chart.
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and follow the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6fc66721bbed763f024563a684b80b96