On the convergence of a class of multilevel methods for large sparse Markov chains

Date
2007
Authors
Buchholz, P.
Dayar, T.
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
SIAM Journal on Matrix Analysis and Applications
Print ISSN
0895-4798
Electronic ISSN
Publisher
Society for Industrial and Applied Mathematics
Volume
29
Issue
3
Pages
1025 - 1049
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Series
Abstract

This paper investigates the theory behind the steady state analysis of large sparse Markov chains with a recently proposed class of multilevel methods using concepts from algebraic multigrid and iterative aggregation- disaggregation. The motivation is to better understand the convergence characteristics of the class of multilevel methods and to have a clearer formulation that will aid their implementation. In doing this, restriction (or aggregation) and prolongation (or disaggregation) operators of multigrid are used, and the Kronecker-based approach for hierarchical Markovian models is employed, since it suggests a natural and compact definition of grids (or levels). However, the formalism used to describe the class of multilevel methods for large sparse Markov chains has no influence on the theoretical results derived. © 2007 Society for Industrial and Applied Mathematics.

Course
Other identifiers
Book Title
Keywords
Aggregation-disaggregation, Kronecker-based numerical techniques, Markov chains, Multigrid, Multilevel methods
Citation
Published Version (Please cite this version)