  We present a novel algorithm to solve a non-linear system of equations, whose
solution can be interpreted as a tight lower bound on the vector of expected
hitting times of a Markov chain whose transition probabilities are only
partially specified. We also briefly sketch how this method can be modified to
solve a conjugate system of equations that gives rise to the corresponding
upper bound. We prove the correctness of our method, and show that it converges
to the correct solution in a finite number of steps under mild conditions on
the system. We compare the runtime complexity of our method to a previously
published method from the literature, and identify conditions under which our
novel method is more efficient.
