A Polynomial-Time Algorithm for the Tridiagonal and Hessenberg P-Matrix   Linear Complementarity Problem
  We give a polynomial-time dynamic programming algorithm for solving the linear complementarity problem with tridiagonal or, more generally, Hessenberg P-matrices. We briefly review three known tractable matrix classes and show that none of them contains all tridiagonal P-matrices. 
Bernd G\"artner, Markus Sprecher
math.OC cs.CC