Diagonal dominance, Schur complements and some classes of H-matrices and P-matrices
Advances in Computational Mathematics
On Iterative Solution for Linear Complementarity Problem with an $H_{+}$-Matrix
SIAM Journal on Matrix Analysis and Applications
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$H$-matrices appear in many areas of science and engineering, e.g., in the solution of the linear complementarity problem (LPC) in optimization theory and in the solution of large systems for real time changes of data in fluid analysis in the car industry. Classical (stationary) iterative methods used for the solution of linear systems have been shown to converge for this class of matrices. Several authors have proposed direct and iterative criteria to identify whether a certain matrix $A \in \mathbb{C}^{n,n}$ is an $H$-matrix. Based on previous and new ideas we propose a new iterative algorithm for irreducible matrices $A$ that, except in a "very special" case, decides whether $A$ is an $H$- or a non $H$-matrix. A MATLAB subroutine is given and numerical examples are provided in support of the theory developed.