Relative-error bounds for the LU decomposition via the GTH algorithm
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- O'Cinneide, C. Numer. Math. (1996) 73: 507. doi:10.1007/s002110050203
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Recently the author showed that the Grassmann-Taksar-Heyman (GTH) algorithm computes the steady-state distribution of a finite-state Markov chain with low relative error. Here it is shown that the LU decomposition computed in the course of the GTH algorithm also has low relative error. The proof requires a refinement of the methods used in the earlier paper.