THE ARITHMETIC MEAN METHOD FOR FINDING THE STATIONARY VECTOR OF MARKOV CHAINS

1 January 1995

journal article
research article
Published by Taylor & Francis in Parallel Algorithms and Applications

Vol. 6 (1) , 25-37
https://doi.org/10.1080/10637199508915496

Abstract

In this paper we extend the arithmetic mean method for large, sparse systems of linear equations to the case where the coefficient matrix is a singular, irreducible M -matrix. Matrices of this kind arise in the computation of the stationary distribution vector for an irreducible Markov chain, as well as in other applications. We report on some numerical experiments on a simple reliability model, where two forms of the arithmetic mean method are compared. The method is well-suited for parallel implementation on a multi-processor.

Keywords

This publication has 14 references indexed in Scilit:

A parallel algorithm for solving block tridiagonal linear systems
Computers & Mathematics with Applications, 1992
A Splitting Method for Large Sparse Linear Systems on a Multivector Computer
Published by Springer Nature ,1991
An iterative method for large sparse linear systems on a vector computer
Computers & Mathematics with Applications, 1990
The arithmetic mean method for solving essentially positive systems on a vector computer^∗
International Journal of Computer Mathematics, 1990
Consistency and Convergence of the Parallel Multisplitting Method for Singular M-Matrices
SIAM Journal on Matrix Analysis and Applications, 1989
Solving large systems of linear ordinary differential equations on a vector computer
Parallel Computing, 1989
Additive polynomial preconditioners for parallel computers
Parallel Computing, 1989
Matrix Methods for Queuing Problems
SIAM Journal on Scientific and Statistical Computing, 1983
Convergent nonnegative matrices and iterative methods for consistent linear systems
Numerische Mathematik, 1978
Convergent Powers of a Matrix with Applications to Iterative Methods for Singular Linear Systems
SIAM Journal on Numerical Analysis, 1977