Iterative Estimations Of Error Bounds For Linear Complementarity Problems Of B-type Matrices

The linear complementarity problems are widely used in the fields of management and control theory,etc,and the error bound estimation of its solution have become a research hotspot.In this thesis,we mainly study the error bound estimation of the so-lutions for linear complementarity problems of two classes of structured matrices:B-matrices and ?1-B matrices,get iterative error estimations respectively,and prove th-at some of them improve existing results.Concretely:Firstly,we study error bounds for linear complementarity problems for B-matrices.By using the infinity norms of the inverse of strictly diagonally dominant M-matrices and according to the grading methods of inequality,we obtain four iterative error esti-mations for linear complementary problems of B-matrices,and prove that the results i?mprove those in[Wang F,Sun D S.New error bounds linear complementary problein-s for B-matrices.Linear and Multilinear Algebra,2017,66(11):2156-2167]and[Li C Q,Gan M T,Yang S R.A new error bound for linear complementarity problems for B-matrices.Electronic Journal of Linear Algebra,2016,31(1):476-484].Secondly,we study the error bounds for linear complementarity problems for ?1-B matrices.By u-sing the infinity norm of the inverse of strictly diagonally dominant M-matrices,we o-btain two error bounds for linear complementary problems of ?1-B matrices.At last,we give some numerical examples to show the effectiveness of the obtained results.