INFORMS Journal on Computing · 1989 · 32 citations · 0 references
Numerical AnalysisNumerical ComputationEngineeringGaussian EliminationHidden Markov ModelDiscrete Dynamical SystemMatrix SolutionsMarkov KernelSystems EngineeringLinear Equations ArisingMatrix MethodComputer ScienceMarkov Chain Monte CarloMatrix AnalysisStochastic Differential EquationLinear Equations
We examine several methods for numerically solving linear equations that arise in the study of Markov chains. These methods are Gaussian elimination, state-reduction, closed-form matrix solutions, and some hybrid methods. The emphasis is on moments of first-passage times and times to absorption. We compare the methods on the basis of accuracy and computation. We conclude that state-reduction is the most accurate and that the matrix solutions have the least computation time. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.