Computing the exponential of large block-triangular block-Toeplitz matrices encountered in fluid queues

被引：22

作者：

Bini, D. A. ^{[1
]}

Dendievel, S. ^{[2
]}

Latouche, G. ^{[2
]}

Meini, B. ^{[1
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, I-56100 Pisa, Italy

[2] Univ Libre Bruxelles, Dept Informat, Brussels, Belgium

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2016年 / 502卷

关键词：

Matrix exponential; Toeplitz matrix; Circulant matrix; Markov generator; Fluid queue; Erlang approximation; DECAY PROPERTIES; PROBABILITIES; ENTRYWISE;

D O I：

10.1016/j.laa.2015.03.035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Erlangian approximation of Markovian fluid queues leads to the problem of computing the matrix exponential of a subgenerator having a block-triangular, block-Toeplitz structure. To this end, we propose some algorithms which exploit the Toeplitz structure and the properties of generators. Such algorithms allow us to compute the exponential of very large matrices, which would otherwise be untreatable with standard methods. We also prove interesting decay properties of the exponential of a generator having a block-triangular, block-Toeplitz structure. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：387 / 419

页数：33

共 21 条

[1] The complex step approximation to the Frechet derivative of a matrix function [J].