  Strong-Disorder Renormalization Group (SDRG), despite being a relatively
simple real-space renormalization procedure, provides in principle exact
results on the critical properties at the infinite-randomness fixed point of
random quantum spin chains. Numerically, SDRG can be efficiently implemented as
a renormalization of Matrix Product Operators (MPO-RG). By considering larger
blocks than SDRG, MPO-RG was recently used to compute non-critical quantities
of finite chains that are inaccessible to SDRG. In this work, the accuracy of
this approach is studied and two simple and fast improvements are proposed. The
accuracy on the ground state energy is improved by a factor at least equal to 4
for the random Ising chain in a transverse field. Finally, the proposed
algorithms are shown to yield Binder cumulants of the 3-color random
Ashkin-Teller chain that are compatible with a second-order phase transition
while a first-order one is predicted by the original MPO-RG algorithm.
