| Linear complementarity problem LCP(M,q)is an important optimization problem.LCP(M,q)is a cross research field between operations research and computational mathematics,and it’s widely used in economics and engineering technology.The existence,uniqueness and stability of the solution of LCP(M,q)are closely related to the structure of matrix M.The solution of LCP(M,q)has excellent properties when matrix M is special matrix.For example,LCP(M,q)has a unique solution if matrix M is a P-matrix.In the actual solution process,the different,algorithms often lead to a certain error between the numerical solution and the real solution.Therefore,how to reduce the error is a very meaningful research topic.Based on the existing conclusions,the error bounds estimation of LCP(M,q)of three kinds of P-type matrices is studied in this paper.Aiming at the error bound estimation of the solution of B-matrix and BS-matrix linear complementarity problem.Based on the range for the infinity norm for the inverse of strictly diagonally dominant M-matrix,according to the definitions and properties of B-matrix and BS-matrix,combined with the scaling technique of inequality,new estimation formulas of the error bound of the solution of the linear complementarity problem for B-matrix and BS-matrix arc obtained respectively.Theoretical analysis and numerical examples verify the feasibility and effectiveness of the new estimation formula of error bound.For the error bound estimation of the solution of weak chain diagonally dominant B-matrix linear complementarity problem.Based on the range for the infinity norm for the inverse of weakly chain diagonally dominant M-matrix,then combine the inequality scaling techniques,a new error bound for the linear complementarity problem when the involved matrix is a weakly chain diagonally dominant M matrix is obtained.Theory analysis and numerical examples verify the feasibility and effectiveness of the new estimation formula of error bound. |
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