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Error bounds for linear complementarity problems of S-QN matrices

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Abstract

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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Acknowledgments

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

Funding

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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Keywords

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