An Algorithmic Characterization of $P$-Matricity
Ibtihel Ben Gharbia, Jean Charles Gilbert · SIAM Journal on Matrix Analysis and Applications · 2013
It is shown that a nondegenerate square real matrix $M$ is a $P$-matrix if and only if, whatever is the real vector $q$, the Newton-min algorithm does not cycle between two points when it is used to solve the linear complementarity problem $0\leqslant x\perp(Mx+q)\geqslant0$.