Equivalence of the fastest apparent convergence criterion and the principle of minimal sensitivity in perturbative quantum chromodynamics

We show that the fastest apparent convergence criterion and the principle of minimal sensitivity, in the next-to-leading and third orders, are equivalent, in the sense that they lead to $n\mathrm{th}$-order approximants whose difference, which is formally of order $n+1\mathrm{}$, carries a numerical coefficient of order unity.