Discussion for H

Nonsingular H-matrices and positive stable matrices play an important role in the stability of neural network system. In this paper, some criteria for nonsingular H-matrices are obtained by the theory of diagonally dominant matrices and the obtained result is introduced into identifying the stability of neural networks. So the criteria for nonsingular H-matrices are expanded and their application on neural network system is given. Finally, the effectiveness of the results is illustrated by numerical examples

ON ITERATIVE SOLUTION FOR LINEAR COMPLEMENTARITY PROBLEM WITH AN H+-MATRIX

The numerous applications of the linear complementarity problem (LCP) in, e.g., the solution of linear and convex quadratic programming, free boundary value problems of fluid mechanics, and moving boundary value problems of economics make its efficient numerical solution a very imperative and interesting area of research. For the solution of the LCP, many iterative methods have been proposed, especially, when the matrix of the problem is a real positive definite or an H+-matrix. In this work we assume that the real matrix of the LCP is an H-vertical bar - matrix and solve it by using a new method, the scaled extrapolated block modulus algorithm, as well as an improved version of the very recently introduced modulus-based matrix splitting modified AOR iteration method. As is shown by numerical examples, the two new methods are very effective and competitive with each other