Symmetric stochastic inverse eigenvalue problem

被引：0

作者：

Zhang, Quanbing ^{[1
]}

Xu, Changqing ^{[2
]}

Yang, Shangjun ^{[3
]}

机构：

[1] Anhui Univ, Minist Educ, Key Lab Intelligent Comp & Signal Proc, Hefei 230039, Anhui, Peoples R China

[2] Suzhou Univ Sci & Technol, Dept Appl Math, Suzhou, Jiangsu, Peoples R China

[3] Anhui Univ, Sch Math Sci, Hefei 230039, Anhui, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2015年

基金：

中国国家自然科学基金;

关键词：

inverse eigenvalue problem; symmetric stochastic inverse eigenvalue problem; typical orthogonal matrix; MATRICES;

D O I：

10.1186/s13660-015-0698-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Firstly we study necessary and sufficient conditions for the constant row sums symmetric inverse eigenvalue problem to have a solution and sufficient conditions for the symmetric stochastic inverse eigenvalue problem to have a solution. Then we introduce the concept of general solutions for the symmetric stochastic inverse eigenvalue problem and the concept of totally general solutions for the 3 x 3 symmetric stochastic inverse eigenvalue problem. Finally we study the necessary and sufficient conditions for the symmetric stochastic inverse eigenvalue problems of order 3 to have general solutions, and the necessary and sufficient conditions for the symmetric stochastic inverse eigenvalue problems of order 3 to have a totally general solution.

引用

页数：17

共 50 条

[41] Numerical solution of the inverse eigenvalue problem for real symmetric Toeplitz matrices
Trench, William F.
SIAM Journal of Scientific Computing, 1997, 18 (06): : 1722 - 1736
[42] A symmetric generalized inverse eigenvalue problem in structural dynamics model updating
Jiang, Jiashang
Dai, Hua
Yuan, Yongxin
LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 439 (05) : 1350 - 1363
[43] A family of realizability criteria for the real and symmetric nonnegative inverse eigenvalue problem
Soto, Ricardo L.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2013, 20 (02) : 336 - 348
[44] The inverse eigenvalue problem for symmetric quasi anti-bidiagonal matrices
Nazari, A. M.
Beiranvand, Z.
APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (23) : 9526 - 9531
[45] An inverse eigenvalue problem and a matrix approximation problem for symmetric skew-hamiltonian matrices
Xie, Dongxiu
Huang, Ningjun
Zhang, Qin
NUMERICAL ALGORITHMS, 2007, 46 (01) : 23 - 34
[46] An inverse eigenvalue problem and a matrix approximation problem for symmetric skew-hamiltonian matrices
Dongxiu Xie
Ningjun Huang
Qin Zhang
Numerical Algorithms, 2007, 46 : 23 - 34
[47] A recursive method for constructing doubly stochastic matrices and inverse eigenvalue problem
Adeli, Iman
Taheri, Maryam
Moghadam, Mahmoud Mohseni
LINEAR ALGEBRA AND ITS APPLICATIONS, 2018, 537 : 318 - 331
[48] On the Inverse Eigenvalue Problem for Irreducible Doubly Stochastic Matrices of Small Orders
Zhang, Quanbing
Xu, Changqing
Yang, Shangjun
ABSTRACT AND APPLIED ANALYSIS, 2014,
[49] A note on the inverse spectral problem for symmetric doubly stochastic matrices
Mourad, Bassam
Abbas, Hassan
Moslehian, Mohammad Sal
LINEAR & MULTILINEAR ALGEBRA, 2015, 63 (12): : 2537 - 2545
[50] A review on the direct and inverse transmission eigenvalue problem for the spherically symmetric refractive index
Pallikarakis, Nikolaos
BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2024, 30 (03):

← 1 2 3 4 5 →