On sufficient and necessary conditions for the Jacobi matrix inverse eigenvalue problem

2004 ◽  
Vol 98 (1) ◽  
pp. 167-176 ◽  
Author(s):  
Linzhang Lu ◽  
Michael K. Ng
Keyword(s):  
Eigenvalue Problem ◽  
Necessary Conditions ◽  
Jacobi Matrix ◽  
Inverse Eigenvalue Problem ◽  
Matrix Inverse ◽  
Sufficient And Necessary Conditions ◽  
Inverse Eigenvalue

Inverse eigenvalue problem for Jacobi matrix and nonnegative matrices

2021 ◽  
pp. 2250098
Author(s):  
Somayeh Zangoei Zadeh ◽  
Azim Rivaz
Keyword(s):  
Eigenvalue Problem ◽  
Jacobi Matrix ◽  
Inverse Eigenvalue Problem ◽  
Nonnegative Matrices ◽  
Inverse Eigenvalue ◽  
Matrix Formula

In this paper, we present a method for constructing a Jacobi matrix [Formula: see text] using [Formula: see text] known eigenvalues [Formula: see text]. Some conditions are also given under which the constructed matrix is nonnegative and its diagonal entries are specified. Finally, we present a technique for constructing symmetric and nonsymmetric nonnegative matrices by their eigenvalues.

scholarly journals Explicit solution for an infinite dimensional generalized inverse eigenvalue problem

2001 ◽  
Vol 26 (9) ◽  
pp. 513-523 ◽  
Author(s):  
Kazem Ghanbari
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Function ◽  
Spectral Data ◽  
Explicit Solution ◽  
Generalized Inverse ◽  
Jacobi Matrix ◽  
Inverse Eigenvalue Problem ◽  
Infinite Dimensional ◽  
Generalized Inverse Eigenvalue Problem ◽  
Inverse Eigenvalue

We study a generalized inverse eigenvalue problem (GIEP),Ax=λBx, in whichAis a semi-infinite Jacobi matrix with positive off-diagonal entriesci>0, andB= diag (b0,b1,…), wherebi≠0fori=0,1,…. We give an explicit solution by establishing an appropriate spectral function with respect to a given set of spectral data.

scholarly journals The Uniqueness of Solution to the Inverse Eigenvalue Problem for an Arrow-shaped Generalised Jacobi Matrix

2021 ◽  
Vol 2068 (1) ◽  
pp. 012014
Author(s):  
Hongliang Huang ◽  
Qike Wang ◽  
Zhibin Li ◽  
Lidong Wang
Keyword(s):  
Eigenvalue Problem ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Jacobi Matrix ◽  
Inverse Eigenvalue Problem ◽  
Mathematical Expressions ◽  
Uniqueness Of The Solution ◽  
Inverse Eigenvalue ◽  
Mathematical Derivation ◽  
The Uniqueness Theorem

Abstract This paper studies the inverse eigenvalue problem for an arrow-shaped generalised Jacobi matrix, inverting matrices through two eigen-pairs. In the paper, the existence and uniqueness of the solution to the problem are discussed, and mathematical expressions as well as a numerical example are given. Finally, the uniqueness theorem of its matrix is established by mathematical derivation.

scholarly journals An Inverse Eigenvalue Problem for Jacobi Matrices

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Zhengsheng Wang ◽  
Baojiang Zhong
Keyword(s):  
Eigenvalue Problem ◽  
Numerical Algorithm ◽  
Jacobi Matrix ◽  
Sufficient Conditions ◽  
Inverse Eigenvalue Problem ◽  
Jacobi Matrices ◽  
Inverse Eigenvalue

A kind of inverse eigenvalue problem is proposed which is the reconstruction of a Jacobi matrix by given four or five eigenvalues and corresponding eigenvectors. The solvability of the problem is discussed, and some sufficient conditions for existence of the solution of this problem are proposed. Furthermore, a numerical algorithm and two examples are presented.

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