Error Bounds for Linear Complementarity Problem of $SD{D_k}$ Matrices (Communications in Mathematical Research, 2025)
$SD{D_k}$ matrices are a subclass of the nonsingular $H$-matrices. The infinity norm of the inverse for $SD{D_k}$ matrices has been given. In the paper, we utilize this result in the context of the linear complementarity problem, and the error bounds of the linear complementarity problem for $SD{D_k}$ matrices are obtained. By the relationship between the $SDD$ matrices and the $SD{D_k}$ matrices, we further obtain the error bounds of the linear complementarity problem for $SDD$ matrices. In addition, it is proved that the bounds presented in this paper are sharper than the well-known bounds under some conditions. Finally, numerical examples are provided to demonstrate the effectiveness of our results.
Keywords: Linear complementarity problem; error bound; $SD{D_k}$ matrices; $SDD$ matrices