On the asymptotic optimality of error bounds for some linear complementarity problems

We introduce strong B-matrices and strong B-Nekrasov matrices, for which some error bounds for linear complementarity problems are analyzed. In particular, it is proved that the bounds of García-Esnaola and Peña (Appl. Math. Lett. 22, 1071–1075, 2009) and of (Numer. Algor. 72, 435–445, 2016) are asymptotically optimal for strong B-matrices and strong B-Nekrasov matrices, respectively. Other comparisons with a bound of Li and Li (Appl. Math. Lett. 57, 108–113, 2016) are performed