The Determination Of Non-singular H-matrix And Its Application In Linear Complementary Problem

Nonsingular H-matrix is a kind of special matrix which plays an important role in the study of basic mathematics theory,economics,biology,electricity,and so on.The beautiful element property of nonsingular H-matrix is commonly used as the condition to determine H-matrix.In this paper,according to the element properties of a-diagonally dominant matrix and ?-chain diagonally dominant matrix,constructing positive diagonal matrix by adding appropriate parameters,use get several criteria for H-matrix,it improve and generalize some existing results.AS an application,we make a further research on the error bounds of linear complementarity problem for SD(a)matrix,and obtain an estimable new error bound of linear complementarity problem.This paper is divided into four chapters.In chapter 1,the research background on judgement of nonsingular H-matrix and error bounds estimate of linear complementarity problem for special matrix,research work of this paper are introduced.In chapter 2,the methods for judging nonsingular H-matrix are studied.According to a-diagonally matrices and a-chain diagonally dominant matrix element properties,the positive diagonal matrix is constructed,the sufficient condition for determining H-matrix are obtained numerical example are illus-trated.In chapter 3,the error bound estimation of linear complementary problem are studied.Using the element property SD(a)matrix and the skills of mag-nifying and shrinking of inequation,a new estimable error bound is obtained and the validity of the new error bound by examples is verified according to the equivalent relation of SD(a)matrix and H-matrix.In chapter 4,the content of this paper is summarized and the future re-search is prospected.