A very simple analysis is provided on the rate of local convergence for a class of high-order infeasible-path-following algorithms for the $P_*$-linear complementarity problem. It is shown that the rate of local convergence of a $\nu$-order algorithm with a centering step is $\nu+1$ if there is a strictly complementary solution and $(\nu+1)/2$ if there is not. For the $\nu$-order algorithm without the centering step the corresponding rates are $\nu$ and $\nu/2$, respectively.
Research Report No. 698, Department of Mathematics, National University of Singapore, 119260, SINGAPORE