Further comparisons of direct methods for computing stationary distributions of Markov chains
SIAM Journal on Algebraic and Discrete Methods
Computing Poisson probabilities
Communications of the ACM
An introduction to mathematical logic and type theory: to truth through proof
An introduction to mathematical logic and type theory: to truth through proof
Bounding the error in Gaussian Elimination for Tridiagonal systems
SIAM Journal on Matrix Analysis and Applications
Computer Arithmetic in Theory and Practice
Computer Arithmetic in Theory and Practice
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
Two finite-difference methods for solving MAP(t)/PH(t)/1/K queueing models
Queueing Systems: Theory and Applications
Computers and Operations Research
A New General-Purpose Method for the Computation of the Interval Availability Distribution
INFORMS Journal on Computing
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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.