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Error bounds for linear complementarity problems of $$B_{\pi }^R$$ B π R -matrices
Computational and Applied Mathematics ( IF 2.5 ) Pub Date : 2021-03-26 , DOI: 10.1007/s40314-021-01491-w
Héctor Orera , Juan Manuel Peña

It is proved that any \(B_{\pi }^R\)-matrix has positive determinant. For \({\pi >0}\), norm bounds for the inverses of \(B_{\pi }^R\)-matrices and error bounds for linear complementarity problems associated with \(B_{\pi }^R\)-matrices are provided. In this last case, the bounds are simpler than previous bounds and also have the advantage that they can be used without previously knowing whether we have a \(B_{\pi }^R\)-matrix. Some numerical examples show that these new bounds can be considerably sharper than previous ones.



中文翻译:

$$ B _ {\ pi} ^ R $$ BπR-矩阵的线性互补问题的误差界

证明任何\(B _ {\ pi} ^ R \)-矩阵都具有正行列式。对于\({\ pi> 0} \)\(B _ {\ pi} ^ R \)的逆的范数界和与\(B _ {\ pi} ^ R \ )-提供了矩阵。在后一种情况下,边界比以前的边界更简单,并且具有以下优点:可以在不事先知道我们是否具有\(B _ {\ pi} ^ R \)-矩阵的情况下使用它们。一些数值示例表明,这些新界限可能比以前的界限更加清晰。

更新日期:2021-03-26
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