Error Bounds For Linear Complementarity Problems Of Three Subclasses Of H-matrices

Linear complementary problems have a wide range of applications in Mathematics,Economics,Mechanics,and other fields.One of the most important problems on linear complementary problems is to bound the error of its solution.In this thesis we study the error bound for the solution of linear complementary problems with ?-SDD ma-trices,?₁-SSD matrices and WDSDD matrices as subclasses of H-matrices.Con-cretely,for the parametric error bound for linear complementary problems with?-SDD matrices in[M.García-Esnaola,J.M.Pe?a.Error bounds for linear complemen-tarity problems with a ?-SDD matrices.Linear Algebra and its Applications,2013,438:1399-1346],we obtain its computable infimum by the relations of?-SDD ma-trices and H-matrices,and the monotonicity of the function of this parameter;for the parametric error bound for ?₁-SSD matrices case,we also obtain its computable infi-mum for the three intervals of the parameter;for the error bound for linear complemen-tary problems with WDSDD matrices,some parametric error bounds are confirmed by the upper bound for the infinity norm of the inverse of strictly diagonally dominant matrices,and the relations of WDSDD matrices and H-matrices.Its computable infi-mum is also obtained.