Abstract
The purpose of this paper is to report on a comparison of an implementation of a simple direct $LU$ factorization method, suggested by Funderlic and Mankin [SIAM J. Sci. Stat. Comput., 2 (1981), pp. 375–383], with other direct methods recommended by Paige, Styan and Wachter [J. Stat. Comput.Simul., 4 (1975), pp. 173–186], for computing stationary distributions of Markov chains. A backward error analysis is developed and conditioning problems are addressed. The method is stable without pivoting, it is numerically efficient and it lends itself to symmetric pivoting to preserve sparsity.
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