(untitled) (Communications in Mathematical Research, 2025)
SDD_k matrices are a subclass of the nonsingular H-matrices. The infinity norm of the inverse for SDD_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 SDD_k matrices are obtained. By the relationship between the SDD matrices and the SDD_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.