Rounding errors in certain algorithms involving Markov chains

Author:

Grassmann Winfried K.1

Affiliation:

1. Univ. of Saskatchewan

Abstract

A number of algorithms involving Markov chains contain no subtractions. This property makes the analysis of rounding errors particularly simple. To show this, some principles for analyzing the propagation and generation of rounding errors in algorithms containing no subtraction are discussed first. These principles are then applied in the context of a simple recursive algorithm involving the transient solution of discrete-time Markov chains, Jensen's algorithm, and state reduction. Jensen's algorithm, also known as randomization or uniformization, is an algorithm for finding transient solutions of continuous-time Markov chains. State reduction is a method for finding equilibrium probabilities for discrete-time or continuous-time Markov chains.

Publisher

Association for Computing Machinery (ACM)

Subject

Applied Mathematics,Software

Reference21 articles.

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3. Backward error analysis for totally positive linear systems;DEBOOR C.;Numer. Math.,1977

4. Computing Poisson probabilities

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