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Upper norm bounds for the inverse of locally doubly strictly diagonally dominant matrices with its applications in linear complementarity problems

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Abstract

In this paper, we present two error bounds for the linear complementarity problems (LCPs) of locally doubly strictly diagonally dominant (LDSDD) matrices. The error bounds are based on two upper norm bounds for the inverse of LDSDD matrices by using a new reduction method. The core of the reduction method lies in the particularity of the LDSDD matrices, which allows us to turn the problem into computing the counterpart of k-order doubly strictly diagonally dominant (DSDD) matrices through partition and summation. Many numerical experiments with lots of random matrices are presented to show the efficiency and superiority of our results.

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Acknowledgements

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

Funding

The work was supported by the National Natural Science Foundation of China (grant no. 11971413) and by the Xiangtan University Innovation Foundation for Postgraduate (grant no. XDCX2022Y067).

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Correspondence to Jianzhou Liu.

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Liu, J., Zhou, Q. & Xiong, Y. Upper norm bounds for the inverse of locally doubly strictly diagonally dominant matrices with its applications in linear complementarity problems. Numer Algor 90, 1465–1491 (2022). https://doi.org/10.1007/s11075-021-01237-z

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