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Volume 11, Issue 3
Norm Estimates for the Inverses of Strictly Diagonally Dominant $M$-Matrices and Linear Complementarity Problems

Yebo Xiong & Jianzhou Liu

DOI: 10.4208/eajam.210820.161120

East Asian J. Appl. Math., 11 (2021), pp. 487-514.

Published online: 2021-05

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  • Abstract

A partition reduction method is used to obtain two new upper bounds for the inverses of strictly diagonally dominant $M$-matrices. The estimates are expressed via the determinants of third order matrices. Numerical experiments with various random matrices show that they are stable and better than the estimates presented in literature. We use these upper bounds in order to improve known error estimates for linear complementarity problems with $B$-matrices.

  • Keywords

Strictly diagonally dominant matrix, $M$-matrix, linear complementarity problem, inverse, infinity norm bound.

  • AMS Subject Headings

15A06, 93C05, 15B99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-11-487, author = {Xiong , Yebo and Liu , Jianzhou}, title = {Norm Estimates for the Inverses of Strictly Diagonally Dominant $M$-Matrices and Linear Complementarity Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {11}, number = {3}, pages = {487--514}, abstract = {

A partition reduction method is used to obtain two new upper bounds for the inverses of strictly diagonally dominant $M$-matrices. The estimates are expressed via the determinants of third order matrices. Numerical experiments with various random matrices show that they are stable and better than the estimates presented in literature. We use these upper bounds in order to improve known error estimates for linear complementarity problems with $B$-matrices.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.210820.161120}, url = {http://global-sci.org/intro/article_detail/eajam/19138.html} }
TY - JOUR T1 - Norm Estimates for the Inverses of Strictly Diagonally Dominant $M$-Matrices and Linear Complementarity Problems AU - Xiong , Yebo AU - Liu , Jianzhou JO - East Asian Journal on Applied Mathematics VL - 3 SP - 487 EP - 514 PY - 2021 DA - 2021/05 SN - 11 DO - http://doi.org/10.4208/eajam.210820.161120 UR - https://global-sci.org/intro/article_detail/eajam/19138.html KW - Strictly diagonally dominant matrix, $M$-matrix, linear complementarity problem, inverse, infinity norm bound. AB -

A partition reduction method is used to obtain two new upper bounds for the inverses of strictly diagonally dominant $M$-matrices. The estimates are expressed via the determinants of third order matrices. Numerical experiments with various random matrices show that they are stable and better than the estimates presented in literature. We use these upper bounds in order to improve known error estimates for linear complementarity problems with $B$-matrices.

Xiong , Yebo and Liu , Jianzhou. (2021). Norm Estimates for the Inverses of Strictly Diagonally Dominant $M$-Matrices and Linear Complementarity Problems. East Asian Journal on Applied Mathematics. 11 (3). 487-514. doi:10.4208/eajam.210820.161120
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