Two Types Of Iterative Algorithm For Linear Complementarity Problem And Related Research

In this paper I consider the MAOR method convergence area for LCP(M,q), the MAOR method for the extended vertical linear complementarity problem, the extended vertical linear complementarity problem, localization of the perron roots of matrices. This paper mainly includes four parts:1. I consider the MAOR method convergence area for LCP(M,q) associate with H-matrix more, where M is nonsingular matrix of the following form: D₁ and D₂ are both square nonsingular diagonal matrices. The results of Ljiljana Cvetkovic and Sanja Rapaji(?) are improved.2. In this part, I mainly consider the existence and uniqueness of the extended vertical linear complementarity problem.3. I proposed the MAOR method and the MSOR method for the EVLCP(M,N,p,q). Forthermore, I give some convergence results of the MAOR method and the MSOR method, when M,N are both M-matrices.4. For a given nonnegative irreducible A, I present a new method that utilizes two sequences, which are both strictly monotone function, to estimate and determine the unique Perron root of A.