Abstract 
    
  This talk will cover two recent papers of the speaker.  
    
  1. We give new error bounds for the linear complementarity problem(LCP) where 
the involved matrix is a P-matrix. Computation of rigorous error bounds can be  
turned into  a  P-matrix linear interval system.  The new error bound  
is sharper than the Mathias-Pang error bound. 
Moreover, for the involved matrix being  an H-matrix with positive diagonals, 
an error bound can be found by solving a linear system of equations. 
   Preliminary numerical results show 
that the proposed error bound is efficient for verifying accuracy 
of approximate solutions. 
    
  2.  We define a new fundamental constant associated with a P-matrix and 
show that this constant  is sharper than the Mathias-Pang constant in deriving   
perturbation bounds for the P-matrix LCP. Moreover, this constant defines a  
  measure of sensitivity of  the solution of the P-matrix LCP.