Schur complement-based error bounds for linear complementarity problems of B_{\pi}^R-matrices

Abstract

An error bound for $B_\pi^{R}$-matrices linear complementarity
problems (LCPs) is given by Garc\'{i}a-Esnaola and Pe\~{n}a in the paper (\emph{Calcolo}, 54(3), 813-822, 2017). However, this bound is not effective for $B_\pi^{R}$-matrices with a non-positive vector $\pi$. In this paper, based on the Schur complement, some error bounds involving a parameter for LCPs of $B_\pi^{R}$-matrices with a non-positive vector $\pi$ are presented, and the optimal values of these error bounds are also determined. Numerical examples are performed to illustrate the effectiveness of the obtained bounds.