The linear complementarity problem (M|q) is to findw andz inR
n
such thatw–Mz=q,w0,z0,w
t
z=0, givenM inR
nn
andq in . Murty''s Bard-type algorithm for solving LCP is modeled as a digraph.Murty''s original convergence proof considered allq inR
n
andM inR
nn
, aP-matrix. We show how to solve more LCP''s by restricting the set ofq vectors and enlarging the class ofM matrices beyondP-matrices.
... [Show full abstract] The effect is that the graph contains an embedded graph of the type considered by Stickney and Watson wheneverM is a matrix containing a principal submatrix which is aP-matrix. Examples are presented which show what can happen when the hypotheses are further weakened.