Error Bound Estimations For The Linear Complementarity Problems Of Some Structured Matrices

The linear complementarity problem was the earliest constraint condition used to optimize the inequality of continuous variables.So far,it has been involved in many fields such as operational research,finance,engineering,etc.And is mainly applied to quadratic programming,optimal stopping problem,elastic contact problem,nonlinear obstacle and free boundary problem,option pricing,space price balance and traffic balance,etc.However,when studying the linear complementarity problem,different structural matrices have different modeling methods,and there will be errors between the numerical solution and the real value,so it is very important to study the error bound estimation of the linear complementarity problem of special structural matrices.Firstly,the research background and significance of linear complementarity problem are briefly described,and the research status of linear complementarity problem is discussed.The symbols,definitions,properties and related lemmas in thesis are given.Secondly,according to the infinity norm of inverse of strictly diagonally dominant M-matrix,a new error bound of linear complementarity problems of B-matrix is obtained,and its effectiveness is demonstrated by theoretical and numerical examples.By means of the characteristics of matrix elements and scaling techniques of inequalities,based on the existing literature,the upper bound estimation formula of the infinite norm of the inverse of the weakly chained diagonally dominant M-matrix is improved,and the error bound of the linear complementarity problems of weakly chained diagonally dominant B-matrix is further optimized according to this estimation formula.Theoretical research and numerical examples show that the estimation formula is superior to some existing results under certain conditions.Then,some inequalities of the element relationship between strictly diagonally dominant M-matrix and its inverse are given,and a new upper bound of the infinite norm of the inverse of strictly diagonally dominant M-matrix is given.By applying these new bounds to the linear complementarity problem,another error bound of the linear complementarity problem of BS-matrix is obtained,and the lower bound of the minimum singular value is given.Theoretical analysis and numerical results show the effectiveness of the calculation results.At last,the whole thesis is summarized,and the problems to be studied in the next step are given.