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M-矩阵最小特征值的新界值估计 被引量：4

New Bounds on the Minimum Eigenvalue of M-Matrices
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摘要 利用著名的Gerschgorin圆盘定理,给出了非负矩阵A与非奇异M-矩阵B的逆矩阵B-1的Hadamard积AB-1的谱半径ρ(AB-1)两个新的上界估计式,利用τ(B)=1ρ(B-1)这一性质,从而得到M-矩阵B最小特征值的两个新下界估计式.算例表明,所得的估计式在一定条件下优于现有的估计式,且这些估计式只依赖于矩阵的元素,容易计算. Two new upper bounds for the spectral radiusρ（A°B-1）for the Hadamard product of a nonnegative matrix A and the inverse of a nonsingular M-matrix B are discussed by applying the famous Gerschgorin disc theorem.On the basis of the results ofτ（B）=1/ρ（B-1）,two new lower bounds of the minimum eigenvalue for a nonsingular M-matrix are obtained.The given numerical example shows that these new formulae improve several existing results in some cases and these new estimating formulae are only depending on the entries of matrix and are easy to calculate.
作者 李玲玲 李华 许伟涛
机构地区 河南城建学院数理学院 河南工业大学信息科学与工程学院
出处 《河南大学学报（自然科学版）》 CAS 2015年第2期134-138,共5页 Journal of Henan University:Natural Science
基金 国家自然科学青年基金(61300123) 河南城建学院校科学研究项目(2014JYB018)
关键词 非负矩阵 M-矩阵 HADAMARD积 谱半径 最小特征值 nonnegative matrix M-matrix Hadamard product spectral radius the minimum eigenvalue
分类号 O151.21 [理学—基础数学]
  • 相关文献

参考文献7

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二级参考文献8

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共引文献1

同被引文献15

  • 1陈现平,王文省.两个矩阵同时对角化的条件[J].枣庄学院学报,2005,22(2):11-13. 被引量：5
  • 2孔庆兰.分块矩阵的应用[J].枣庄学院学报,2006,23(5):24-26. 被引量：2
  • 3陈景良,陈向晖.特殊矩阵[M].北京:清华大学出版社,2000.130.
  • 4Chaoqian L, Yaotang LI, Ruijuan Z. New inequalities for the minimum eigenvalue of M -matrices [ J ]. Linear and Multilin- ear Algebra, 2013,61 (9) : 1267 - 1279.
  • 5Horn R A, Johnson C R. Topics in Matrix Analysis[ M ]. New York:Cambridge University Press, 1991.
  • 6Sheng C. A Lower bound for the minimum eigenvalue of the Hadamard product of matrix[ J ]. Linear Algebra Appl,200d (378) :159 - 166.
  • 7Rong H. Some inequalities for the Hadamard product and the Fan product of matrices[ J]. Linear Algebra and its Applica- tions ,2008,428 : 1551 - 1559.
  • 8HUANG Rong.Some inequalities for the Hadamard product and the Fan product of matrices[J].Linear Algebra and its Applications, 2008,428: 1551-1559.
  • 9HORN R A,JOHNSON C R.Matrix analysis[M].Cambridge:Cambridge University Press, 1995.
  • 10LI Chaoqian,LI Yaotang,ZHAO Ruijuan.New inequalities for the minimum eigenvalue of Mmatrices[J]. Linear and Multilinear Algebra, 2013,61 (9) : 1267-1279.

引证文献4

二级引证文献1

河南大学学报（自然科学版）
2015年 第2期

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