一类非奇异H-矩阵快速迭代判定新算法
A New Algorithm of Fast Iterative Criterion for Non-Singular H-Matrices
DOI: 10.12677/AAM.2019.81011, PDF,    国家自然科学基金支持
作者: 陈 茜, 庹 清:吉首大学数学与统计学院,湖南 吉首
关键词: 非奇异H-矩阵迭代矩阵迭代算法
摘要: 通过对迭代矩阵因子和收敛条件的改进,得到一组非奇异H-矩阵新的快速迭代判定算法,并从理论上说明了算法的收敛性。最后,利用Matlab数值仿真实验结果表明所得算法迭代收敛速度更快,稳定性更好。
Abstract: By improving the iterative matrix factors and convergence conditions, a new fast iterative criterion algorithm for non-singular H-matrices is obtained, and the convergence of the algorithm is theoretically explained. Finally, the results of Matlab numerical simulation experiments show that the proposed algorithm has faster convergence and better stability.
文章引用:陈茜, 庹清. 一类非奇异H-矩阵快速迭代判定新算法[J]. 应用数学进展, 2019, 8(1): 96-104. https://doi.org/10.12677/AAM.2019.81011

参考文献

[1] Ojiro, K., Niki, H. and Usui, M. (2003) A New Criterion for the H-Matrix Property. Journal of Computational and Ap-plied Mathematics, 150, 293-302.
[Google Scholar] [CrossRef
[2] Kohno, T., et al. (2000) An Iterative Test for H-Matrices. Journal of Computational and Applied Mathematics, 115, 349-355.
[Google Scholar] [CrossRef
[3] Liu, J.Z. and He, A.Q. (2006) A New Algorithmic Charac-terization of H-Matrices. Applied Mathematics and Computation, 183, 603-609.
[Google Scholar] [CrossRef
[4] Liu, J.Z. and He, A.Q. (2007) An Iterleaved Iterative Criterion for H-Matrices. Applied Mathematics and Computation, 186, 727-734.
[Google Scholar] [CrossRef
[5] 周伟伟, 徐仲, 等. 非奇H-矩阵细分迭代判定准则[J]. 数值计算与计算机应用, 2011, 32(4): 293-300.
[6] 张骁, 陆全, 等. 非奇H-矩阵的一组迭代判别法[J]. 2015, 36(1): 59-68.
[7] 丁碧文, 刘建州. H-矩阵的判别法及其迭代算法[J]. 应用数学学报, 2013, 36(5): 935-948.
[8] Gao, Y.-M. and Wang, X.-H. (1992) Criteria for Generalized Diagonally Dominant Matrices and M-Matrices. Linear Algebra and its Applications, 169, 257-268.
[Google Scholar] [CrossRef
[9] 沈光星. 非奇异H阵的新判据[J]. 工程数学学报, 1998(4): 23-29.
[10] 庹清, 朱砾, 刘建州. 一类非奇异H-矩阵判定的新条件[J]. 计算数学, 2008(2): 177-182.