Abstract
The $$P(\tau ,\alpha ,\beta )$$ -pair defined in this paper is a class of matrix pair which is broad enough to include $$P^*$$ -matrix as special case. We construct a combined homotopy equation for the horizontal linear complementarity problem, prove the existence, boundedness and the convergence of the homotopy path, which is from any interior point to the solution of the problem, under a condition that the matrix pair is $$P(\tau ,\alpha ,\beta )$$ pair. Numerical examples show that this method is feasible and effective.
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