New error bounds involving a parameter for linear complementarity problems are presented when the involved matrices are \(B_\pi ^{R}\)-matrices, and the optimal values of these error bounds are determined completely by using the monotonicity of functions of this parameter. It is shown that the optimal error bounds are sharper than that provided by García-Esnaola and Peña (Calcolo 54(3):813–822, 2017) under certain assumptions.

中文翻译：

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$$ B_ \ pi ^ {R} $$ BπR-矩阵的线性互补问题的参数化误差界及其最优值

当所涉及的矩阵是\（B_ \ pi ^ {R} \）-矩阵时，给出了涉及线性互补问题的参数的新误差范围，并且利用该函数的单调性完全确定了这些误差范围的最佳值。参数。结果表明，在某些假设下，最佳误差范围比García-Esnaola和Peña（Calcolo 54（3）：813–822，2017）所提供的范围更尖锐。