On an inverse problem for two spectra of finite Jacobi matrices

2012 ◽  
Vol 218 (14) ◽  
pp. 7573-7589 ◽  
Author(s):  
Gusein Sh. Guseinov
Keyword(s):  
Inverse Problem ◽  
Jacobi Matrices

scholarly journals Dynamic inverse problem for Jacobi matrices

2019 ◽  
Vol 13 (3) ◽  
pp. 431-447 ◽  
Author(s):  
Alexandr Mikhaylov ◽  
◽  
Victor Mikhaylov ◽  
Keyword(s):  
Inverse Problem ◽  
Jacobi Matrices ◽  
Dynamic Inverse ◽  
Dynamic Inverse Problem

Inverse problem about two-spectra for finite Jacobi matrices with zero diagonal

2016 ◽  
Vol 24 (6) ◽  
Author(s):  
Adil Huseynov
Keyword(s):  
Inverse Problem ◽  
Finite Order ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Jacobi Matrices ◽  
The Matrix ◽  
Explicit Procedure ◽  
Necessary And Sufficient

AbstractThe necessary and sufficient conditions for solvability of the inverse problem about two-spectra for finite order real Jacobi matrices with zero-diagonal elements are established. An explicit procedure of reconstruction of the matrix from the two-spectra is given.

scholarly journals On the M-matrix inverse problem for singular and symmetric Jacobi matrices

2012 ◽  
Vol 24 ◽  
Author(s):  
Angeles Carmona ◽  
Andres Encinas ◽  
Margarida Mitjana
Keyword(s):  
Inverse Problem ◽  
Jacobi Matrices ◽  
Matrix Inverse

scholarly journals CAPACITIES AND JACOBI MATRICES

2003 ◽  
Vol 46 (3) ◽  
pp. 719-745 ◽  
Author(s):  
Ahmed Sebbar ◽  
Thérèse Falliero
Keyword(s):  
Inverse Problem ◽  
Chebyshev Polynomials ◽  
Jacobi Matrix ◽  
Symmetric Matrix ◽  
Finite Union ◽  
Conformal Mappings ◽  
Subject Classification ◽  
Jacobi Matrices ◽  
Closed Intervals ◽  
Primary 31B15

AbstractIn this paper, we use the theorem of Burchnall and Shaundy to give the capacity of the spectrum $\sigma(A)$ of a periodic tridiagonal and symmetric matrix. A special family of Chebyshev polynomials of $\sigma(A)$ is also given. In addition, the inverse problem is considered: given a finite union $E$ of closed intervals, we study the conditions for a Jacobi matrix $A$ to exist satisfying $\sigma(A)=E$. We relate this question to Carathéodory theorems on conformal mappings.AMS 2000 Mathematics subject classification: Primary 31B15; 30C20; 39A70

An inverse problem for periodic Jacobi matrices

1970 ◽  
Vol 8 (3) ◽  
pp. 639-645
Author(s):  
I. V. Stankevich
Keyword(s):  
Inverse Problem ◽  
Jacobi Matrices

scholarly journals On a Discrete Inverse Problem for Two Spectra

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Gusein Sh. Guseinov
Keyword(s):  
Inverse Problem ◽  
Spectral Problem ◽  
Finite Order ◽  
Inverse Spectral Problem ◽  
Jacobi Matrix ◽  
Jacobi Matrices ◽  
Symmetric Matrices ◽  
The Matrix ◽  
Inverse Spectral

A version of the inverse spectral problem for two spectra of finite-order real Jacobi matrices (tridiagonal symmetric matrices) is investigated. The problem is to reconstruct the matrix using two sets of eigenvalues: one for the original Jacobi matrix and one for the matrix obtained by deleting the last row and last column of the Jacobi matrix.

scholarly journals The M-matrix inverse problem for singular and symmetric Jacobi matrices

2012 ◽  
Vol 436 (5) ◽  
pp. 1090-1098 ◽  
Author(s):  
E. Bendito ◽  
A. Carmona ◽  
A.M. Encinas ◽  
M. Mitjana
Keyword(s):  
Inverse Problem ◽  
Jacobi Matrices ◽  
Matrix Inverse
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