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.