NASA Logo

NTRS

NTRS - NASA Technical Reports Server

Collections About News Help Login
Back to Results
The condition of a finite Markov chain and perturbation bounds for the limiting probabilitiesThe inequalities bounding the relative error the norm of w- w squiggly/the norm of w are exhibited by a very simple function of E and A. Let T denote the transition matrix of an ergodic chain, C, and let A = I - T. Let E be a perturbation matrix such that T squiggly = T - E is also the transition matrix of an ergodic chain, C squiggly. Let w and w squiggly denote the limiting probability (row) vectors for C and C squiggly. The inequality is the best one possible. This bound can be significant in the numerical determination of the limiting probabilities for an ergodic chain. In addition to presenting a sharp bound for the norm of w-w squiggly/the norm of w an explicit expression for w squiggly will be derived in which w squiggly is given as a function of E, A, w and some other related terms.
Document ID
19790015553
Acquisition Source
Legacy CDMS
Document Type
Other
Authors
Meyer, C. D., Jr. (North Carolina State Univ. Raleigh, NC, United States)
Date Acquired
September 4, 2013
Publication Date
May 1, 1979
Subject Category
Numerical Analysis
Accession Number
79N23724
Funding Number(s)
CONTRACT_GRANT: NSF MCS-76-11989
CONTRACT_GRANT: NSG-1532
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

Related Records

There are no records associated with this record.
No Preview Available