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Error bounds for linear complementarity problems of \(B_{\pi }^R\)-matrices

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Abstract

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.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad de Zaragoza, Zaragoza, Spain

    Héctor Orera

  2. Departamento de Matemática Aplicada/IUMA, Universidad de Zaragoza, Zaragoza, Spain

    Juan Manuel Peña

Authors
  1. Héctor Orera
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  2. Juan Manuel Peña
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Correspondence to Héctor Orera.

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Communicated by Jinyun Yuan.

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This work was partially supported through the Spanish research Grant PGC2018-096321-B-I00 (MCIU/AEI), by Gobierno de Aragón (E41-17R) and Feder 2014-2020 “Construyendo Europa desde Aragón”.

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Orera, H., Peña, J.M. Error bounds for linear complementarity problems of \(B_{\pi }^R\)-matrices. Comp. Appl. Math. 40, 94 (2021). https://doi.org/10.1007/s40314-021-01491-w

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  • DOI: https://doi.org/10.1007/s40314-021-01491-w

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