Circulant preconditioners for stochastic automata networks
type: Item
instance of: scholarly article
title: Circulant preconditioners for stochastic automata networks
zbMATH Open document ID: 0964.65034
published in: Numerische Mathematik
publication date: 2001-06-26T00:00:00Z
full work available at URL: http://hdl.handle.net/10722/75198
review text: The authors consider circulant preconditioners for stochastic automata networks (SANs). Circulant matrices have shown to be a good preconditioners for Toeplitz systems in many applications and in particular, in queueing networks. If only one of the automata is large in size compared to the others, then the authors prove that the preconditioned system of the normal equations will converge very fast. The preconditioned system is solved by conjugate gradient type methods. Three practical SANs are considered and the proposed preconditioning method are compared with the classical method, the block Gauss-Seidel method: Overflow queueing systems, telecommunication systems and a manufacturing system.
reviewed by: Iulian Coroian
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 60K30
zbMATH DE Number: 1545476
zbMATH Keywords: iterative solutions
zbMATH Keywords: preconditioning
zbMATH Keywords: stochastic automata networks
zbMATH Keywords: Toeplitz matrices
zbMATH Keywords: circulant matrices
zbMATH Keywords: queueing networks
zbMATH Keywords: normal equations
zbMATH Keywords: conjugate gradient type methods
zbMATH Keywords: block Gauss-Seidel method
zbMATH Keywords: overflow queueing systems
zbMATH Keywords: telecommunication systems
zbMATH Keywords: manufacturing system
author: Raymond H. Chan
author: Wai-Ki Ching
MaRDI profile type: Publication
OpenAlex ID: W2068712394
DOI: 10.1007/S002110000173
description: scientific article; zbMATH DE number 1545476