Error Bounds For Linear Complementarity Problems Involving Three Subclass Matrices Of P-matrices

Since the linear complementarity problem was first proposed in the 1960s,it has been widely used in mathematical theory and practical application,such as double matrix game,equilibrium problem,space price,contact mechanics and fracture mechanics.So solving linear complementarity problem has very important research value,but in the process of solving,there is a certain error between the numerical solution obtained by different algorithms and its real solution,so we need to reduce the error to ensure the accuracy of linear complementarity problem solution.In this paper,we mainly study the error bounds of solutions for linear complementarity problems of three subclasses of P-matrices.The full paper contains four chapters.The first chapter introduces the research background and its significance.There are also including the main content of each chapter and some prepared knowledge.From the second chapter to the fourth chapter are the main parts of studying.By using the upper bound of the infinite norm of the inverse matrix of strictly diagonally dominant M-matrix and weakly chained diagonally dominant M-matrix,then combine the inequality scaling techniques,and end up with the error bounds for linear complementarity problem of three subclasses of P-matrix:B-matrix,BS-matrix and weakly chained diagonally dominant B-matrix.Finally,the theoretical analysis shows that the new estimation is better than some existing estimations and the numerical examples further verifies the effectiveness of the new estimations.