New error bounds for linear complementarity problems of \(\Sigma \)-SDD matrices and \(SB\)-matrices. (English) Zbl 1442.65101
Summary: A new error bound for the linear complementarity problem (LCP) of \(\Sigma \)-SDD matrices is given, which depends only on the entries of the involved matrices. Numerical examples are given to show that the new bound is better than that provided by M. García-Esnaola and J. M. Peña [Linear Algebra Appl. 438, No. 3, 1339–1346 (2013; Zbl 1261.90064)] in some cases. Based on the obtained results, we also give an error bound for the LCP of \(SB\)-matrices. It is proved that the new bound is sharper than that provided by P.-F. Dai et al. [Numer. Algorithms 61, No. 1, 121–139 (2012; Zbl 1266.65090)] under certain assumptions.
MSC:
| 65K05 | Numerical mathematical programming methods |
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
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