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Error bounds for linear complementarity problems of S-QN matrices

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Linear complementarity problem (LCP) presents many nice properties when the associated matrix belongs to some special matrix classes, especially H-matrices. In this paper, we put forward a new subclass of H-matrices, called S-QN matrices, which is the proper generalization of the QN matrices. We have proved that for a given S-QN matrix A, there exists a diagonal scaling matrix W such that AW is a QN matrix. Then, we present two kinds of error bounds for LCP of S-QN matrices. The Error Bound I generalizes the error bound for LCP of QN matrices. The Error Bound II overcomes the limitation that the Error Bound I cannot be used. Numerical examples illustrate that the Error Bound I is better than other previous bounds for H-matrices in some cases. Moreover, in some special cases, the Error Bound II can improve considerably the Error Bound I.

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The authors are thankful to the anonymous referees for their valuable comments to improve the paper.


The work was supported by the National Natural Science Foundation of China (11671318).

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Correspondence to Ge Li.

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Li, J., Li, G. Error bounds for linear complementarity problems of S-QN matrices. Numer Algor 83, 935–955 (2020). https://doi.org/10.1007/s11075-019-00710-0

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  • Linear complementarity problem
  • H-matrix
  • S-SDD matrix
  • QN matrix
  • S-QN matrix