摘要
广义Nekrasov(非奇异H-矩阵)矩阵在经济数学、控制理论、数值代数等诸多领域中发挥了重要的作用,本文研究了广义Nekrasov矩阵的判定条件问题。从矩阵的元素出发,利用不等式放缩的方法,构造正对角矩阵因子,给出了广义Nekrasov矩阵几种新的判别方法,推广了一些已有的结果.最后用数值算例证明了所得结论的有效性。
关键词: Nekrasov矩阵;非奇异H-矩阵;广义Nekrasov矩阵
Abstract
Generalized Nekrasov(non-singular H-matrix) matrix plays an important role in many fields such as economic mathematics, control theory, numerical algebra, etc. In this paper, the decision conditions of generalized Nekrasov matrix are studied. Starting from the elements of matrix, the positive diagonal matrix factors are constructed by means of inequality reduction, and several new discriminant methods for generalized Nekrasov matrix are given. Finally, a numerical example is used to illustrate the validity of the conclusion.
Key words: Nekrasov matrix; Non-singular H-matrix; Generalized Nekrasov matrix
参考文献 References
[1] Li W.On Nekrasov matrices[J].Linear Algebra Appl,1998,28(1): 87-96.
[2] Pang MX,Zhu XL.Generalized Nekrasov matrices and applications[J].Journal of Computation Mathematics, 2003, 21(2): 183-188.
[3] Wang Q,Song YZ,Li WC.Estimates of upper bounds of the spectral radius for some iteration matrices[J].Journal of Nanjing university mathematical biquarteraly, 2005, 2(2): 96-106.
[4] Kolotilina LY.Bounds or the determinants of Nekrasov and S-Nekrasov matrices[J].Journal of Mathematical Sciences, 2015, 207(5): 776-785.
[5] Esnaola MJ,Pena JM.Error bounds for linear complementarity problems of Nekrasov matrices[J].Numerical Algorithms, 2014, 6(7): 655-667.
[6] Liu JZ,Zhang J,Zhou LX and Tu G.The Nekrasov diagonally dominant degree on the Schur complement of Nekrasov matrices and its applications[J].Applied Mathematics and Computation, 2018, 320: 251-263.
[7] 黎稳,黄廷祝.关于非奇异性判别的Gudkov定理[J].工程数学学报,2009(4):697-702.
[8] 郭爱丽,刘建州.广义Nekrasov矩阵的判定[J].工程数学学报,2009(4):697-702.
[9] 王银燕,徐仲,陆全.广义Nekrasov矩阵的选代判定准则[J].高等学校计算数学学报,2015,37(1):19-30.
[10] 郭爱丽,刘建州.广义Nekrasov矩阵的新判据[J].数学实践与认识,2016,46(5):239-245.
[11] 郭爱丽,左建军.广义Nekrasov矩阵的判别法及其选代算法[J].高校应用数学学报,2020,35(3):356-366.
[12] 吕振华,孙旭,田万福等.广义Nekrasov矩阵的一组改进的判别条件.数值计算与计算机应用,2022,43(3):307-313.
[13] 郭爱丽,左建军.广义Nekrasov矩阵判定的新条件[J].高等学校计算数学学报,2022, 44(2):136-146.