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基于递进结构的广义Nekrasov矩阵的判定
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Abstract:
本文通过递进结构选取正对角矩阵因子的元素，利用Nekrasov矩阵的性质以及不等式的放缩技巧，给出了一类新的Nekrasov矩阵的判定方法。
This article presents a new method for determining a class of Nekrasov matrices by selecting the elements of diagonal matrix factors through a progressive structure, utilizing the properties of Nekrasov matrices and scaling techniques of inequalities.
| [1] | Li, W. (1998) On Nekrasov Matrices. Linear Algebra and Its Applications, 281, 87-96. https://doi.org/10.1016/s0024-3795(98)10031-9 |
| [2] | Lyu, Z., Zhou, L.X. and Liu, J.Z. (2021) A Generalization of S-Nekrasov Matrices. Journal of Mathematical Inequalities, 15, 1093-1100. https://doi.org/10.7153/jmi-2021-15-74 |
| [3] | Li, C., Liu, Q., Gao, L. and Li, Y. (2015) Subdirect Sums of Nekrasov Matrices. Linear and Multilinear Algebra, 64, 208-218. https://doi.org/10.1080/03081087.2015.1032198 |
| [4] | Liu, J., Zhang, J., Zhou, L. and Tu, G. (2018) The Nekrasov Diagonally Dominant Degree on the Schur Complement of Nekrasov Matrices and Its Applications. Applied Mathematics and Computation, 320, 251-263. https://doi.org/10.1016/j.amc.2017.09.032 |
| [5] | Peña, J.M. (2010) Diagonal Dominance, Schur Complements and Some Classes of H-Matrices and P-Matrices. Advances in Computational Mathematics, 35, 357-373. https://doi.org/10.1007/s10444-010-9160-5 |
| [6] | 高磊, 井霞, 王亚强. S-Nekrasov矩阵的逆矩阵无穷范数的新上界[J]. 高等学校计算数学学报, 2018, 40(2): 97-109. |
| [7] | 李艳艳. Nekrasov矩阵的线性互补问题含参数的上界[J]. 文书学院学报, 2023, 37(5): 63-66. |
| [8] | 郭爱丽, 刘建州. 广义Nekrasov矩阵的充分条件[J]. 数学的实践与认识, 2013, 43(3): 189-195. |
| [9] | 郭爱丽, 刘建州. 广义Nekrasov 矩阵的判定[J]. 工程数学学报, 2009, 26(4): 697-702. |
| [10] | 郭爱丽, 周立新. 广义Nekrasov矩阵的一类递进判别法[J]. 重庆工商大学学报: 自然科学版, 2014, 31(2): 30-36. |
| [11] | 石玲玲, 徐仲, 陆全, 等. 广义Nekrasov 矩阵的新迭代判别法[J]. 数值计算与计算机应用, 2013, 34(2): 117-122. |
| [12] | 石玲玲. 广义Nekrasov矩阵的一组细分迭代判定条件[J]. 数学的实践与认识, 2018, 48(8): 227-232. |
