Error Bounds Estimations For The Linear Complementarity Problems Of Several Special Matrices

The linear complementarity problem is a fundamental problem in mathematical modeling.It has wide applications in scientific computing,economics,engineering.After years of research and development,the complementarity problem has expanded from its classical form to various forms in different directions,such as the vertical linear complementarity problem,the horizontal linear complementarity problem and the generalized vertical linear complementarity problem.This article not only studies the error bounds of the linear complementarity problem for special matrices,such as the matrix and the matrix,but also studies the error bounds of the extended vertical linear complementarity problem for DZ-type matrices.For the estimation of the error bounds of the S-SDDS-B matrix and the S-SOB-B matrix linear complementarity problem,the matrix is split into the form of B++C based on the characteristics of its elements.Then,the upper bound of(?)‖(I-D+DA)-1‖∞ is obtained by combining the infinite norm upper bound estimation of the inverse of the S-SDDS matrix and the S-SOB matrix with the scaling method of inequalities.The theoretical proof shows that the obtained results are better than some existing results,and numerical examples demonstrate the validity of the results.For the error bound estimation of the extended vertical linear complementarity problem of DZ-type matrices,the properties of DZ-type matrices are used to prove that the block matrix composed of DZ-type matrices has the row W-property.Then,the error bound of the extended vertical linear complementarity problem of DZtype matrices is obtained,and the rationality of the results is demonstrated through numerical examples.