随机矩阵非1特征值的新包含区域
The New Inclusion Region of Eigenvalue Different from 1 for a Stochastic Matrix

作者: 周宝星 * , 李耀堂 :云南大学,数学与统计学院,云南 昆明; 卫慧芳 :云南财经大学,统计与数学学院,云南 昆明;

关键词: 随机矩阵&alpha1-矩阵非1特征值 &alpha-型特征值包含定理Stochastic Matrices &alpha1-Matrices Eigenvalue Different from 1 &alpha-Eigenvalue Inclusion Theorem

摘要:
利用-型特征值包含定理及修正矩阵,给出随机矩阵两个新的非1特征值包含区域,并由此得到随机矩阵非奇异的两个新的充分条件。数值例子表明,在某些情况下所得结果改进了几个已有结果。

Abstract: Two new inclusion regions of eigenvalue different from 1 of stochastic matrices are given by using the -eigenvalue inclusion theorem and the theory of modified matrices; and two new sufficient conditions of stochastic matrices nonsingular are obtained. Numerical examples are given to show that the existing results are improved in some cases.

文章引用: 周宝星 , 卫慧芳 , 李耀堂 (2016) 随机矩阵非1特征值的新包含区域。 理论数学, 6, 361-367. doi: 10.12677/PM.2016.64051

参考文献

[1] Horn, R.A. and Johnson, C.R. (1986) Matrix Analysis. Cambridge University Press, Cambridge, England.

[2] Seneta, E. (2004) Nonnegative Matrices and Markov Chains. Springer-Verlag, Berlin.

[3] Cvetković, L., Kostic, V. and Pena, J.M. (2011) Eigenvalue Localization Refinements for Matrices Related to Positivity. SIAM Journal on Matrix Analysis and Applications, 32, 771-784. http://dx.doi.org/10.1137/100807077

[4] Varga, R.S. (2004) Gersgorin and His Circles. Springer-Verlag, Berlin. http://dx.doi.org/10.1007/978-3-642-17798-9

[5] Cvetkovic, L., Kostic, V. and Varga, R.S. (2004) A New Gersgorin-Type Eigenvalue Inclusion Set. Electronic Transactions on Numerical Analysis, 18, 73-80.

[6] Shen, S.Q., Yu, J. and Huang, T.Z. (2014) Some Classes of Nonsingular Matrices with Applications to Localize the Real Eigenvalues of Real Matrices. Linear Algebra and Its Applications, 447, 74-87. http://dx.doi.org/10.1016/j.laa.2013.02.005

[7] Li, C.Q., Liu, Q.B. and Li, Y.T. (2014) Gersgorin-Type and Brauer-Type Eigenvalue Localization Sets of Stochastic Matrices. Linear and Multilinear Algebra.

[8] Cvetković, L. (2007) H-Matrix Theory vs. Eigenvalue Localization. Numerical Algorithms, 42, 229-245.

分享
Top