New criteria for nonsingular $ H $-matrices

Panpan Liu; Haifeng Sang; Min Li; Guorui Huang; He Niu; Panpan Liu; Haifeng Sang; Min Li; Guorui Huang; He Niu

doi:10.3934/math.2023893

AIMS Mathematics

2023, Volume 8, Issue 8: 17484-17502. doi: 10.3934/math.2023893

Previous Article Next Article

Research article

New criteria for nonsingular $ H $-matrices

School of Mathematics and Statistics, Beihua University, Jilin 132013, China

Received: 06 March 2023 Revised: 27 April 2023 Accepted: 07 May 2023 Published: 19 May 2023
MSC : 15A57

In this paper, according to the theory of two classes of $ \alpha $-diagonally dominant matrices, the row index set of the matrix is divided properly, and then some positive diagonal matrices are constructed. Furthermore, some new criteria for nonsingular $ H $-matrix are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed criteria.
- diagonally dominant matrix,
- $ \alpha $-diagonally dominant matrix,
- nonsingular $ H $-matrix,
- criteria,
- numerical examples
Citation: Panpan Liu, Haifeng Sang, Min Li, Guorui Huang, He Niu. New criteria for nonsingular $ H $-matrices[J]. AIMS Mathematics, 2023, 8(8): 17484-17502. doi: 10.3934/math.2023893

Related Papers:

Abstract

In this paper, according to the theory of two classes of $ \alpha $-diagonally dominant matrices, the row index set of the matrix is divided properly, and then some positive diagonal matrices are constructed. Furthermore, some new criteria for nonsingular $ H $-matrix are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed criteria.

References

[1]	R. Bru, C. Corral, I. Giménez, J. Mas, Classes of general $H$-matrices, Linear Algebra Appl., 429 (2008), 2358–2366. https://doi.org/10.1016/j.laa.2007.10.030 doi: 10.1016/j.laa.2007.10.030
[2]	M. Alanelli, A. Hadjidimos, On iterative criteria for $H$- and non-$H$-matrices, Appl. Math. Comput., 188 (2007), 19–30. https://doi.org/10.1016/j.amc.2006.09.089 doi: 10.1016/j.amc.2006.09.089
[3]	A. Berman, R. Plemmons, Nonnegative matrices in the mathematical sciences, Philadelphia: SIAM Press, 1994. https://doi.org/10.1137/1.9781611971262
[4]	J. Zhao, Q. Liu, C. Li, Y. Li, Dashnic-Zusmanovich type matrices: a new subclass of nonsingular $H$-matrices, Linear Algebra Appl., 552 (2018), 277–287. https://doi.org/10.1016/j.laa.2018.04.028 doi: 10.1016/j.laa.2018.04.028
[5]	M. Li, Y. Sun, Practical criteria for $H$-matrices, Appl. Math. Comput., 211 (2009), 427–433. https://doi.org/10.1016/j.amc.2009.01.083 doi: 10.1016/j.amc.2009.01.083
[6]	Y. Sun, Sufficient conditions for generalized diagonally dominant matrices (Chinese), Numerical Mathematics A Journal of Chinese Universities, 19 (1997), 216–223.
[7]	Y. Sun, An improvement on a theorem by ostrowski and its applications (Chinese), Northeastern Math. J., 7 (1991), 497–502.
[8]	L. Wang, B. Xi, F. Qi, Necessary and sufficient conditions for identifying strictly geometrically $\alpha$-bidiagonally dominant matrices, U.P.B. Sci. Bull. Series A, 76 (2014), 57–66.
[9]	J. Li, W. Zhang, Criteria for H-matrices (Chinese), Numerical Mathematics A Journal of Chinese Universities, 21 (1999), 264–268.
[10]	R. Jiang, New criteria for nonsingular H-matrices (Chinese), Chinese Journal of Engineering Mathematics, 28 (2011), 393–400.
[11]	G. Han, C. Zhang, H. Gao, Discussion for identifying $H$-matrices, J. Phys.: Conf. Ser., 1288 (2019), 012031. https://doi.org/10.1088/1742-6596/1288/1/012031 doi: 10.1088/1742-6596/1288/1/012031
[12]	X. Chen, Q. Tuo, A set of new criteria for nonsingular $H$-matrices (Chinese), Chinese Journal of Engineering Mathematics, 37 (2020), 325–334.
[13]	T. Gan, T. Huang, Simple criteria for nonsingular $H$-matrices, Linear Algebra Appl., 374 (2003), 317–326. https://doi.org/10.1016/S0024-3795(03)00646-3 doi: 10.1016/S0024-3795(03)00646-3
[14]	T. Gan, T. Huang, Practical sufficient conditions for nonsingular $H$-matrices (Chinese), Mathematica Numerica Sinica, 26 (2004), 109–116.
[15]	Q. Tuo, L. Zhu, J. Liu, One type of new criteria conditions for nonsingular $H$-matrices (Chinese), Mathematica Numerica Sinica, 30 (2008), 177–182.
[16]	Y. Yang, M. Liang, A new type of determinations for nonsingular $H$-matrices (Chinese), Journal of Hexi University, 37 (2021), 20–25. https://doi.org/10.13874/j.cnki.62-1171/g4.2021.02.004 doi: 10.13874/j.cnki.62-1171/g4.2021.02.004
[17]	J. Liu, J. Li, Z. Huang, X. Kong, Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices, Linear Algebra Appl., 428 (2008), 1009–1030. https://doi.org/10.1016/j.laa.2007.09.008 doi: 10.1016/j.laa.2007.09.008
[18]	L. Cvetković, $H$-matrix theory vs. eigenvalue localization, Numer. Algor., 42 (2006), 229–245. https://doi.org/10.1007/s11075-006-9029-3 doi: 10.1007/s11075-006-9029-3

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)