Rec entry the author showed that the Grassmann-Taksar-Heyman (GTH) alg
orithm computes the steady-state distribution of a finite-state Markov
chain with low relative error, Here it is shown that the LU decomposi
tion computed in the course of the GTH algorithm also has low relative
error. The proof requires a refinement of the methods used in the ear
lier paper.