An Inverse Eigenvalue Problem for Jacobi Matrices

Jacobi Matrices ◽

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.

An inverse eigenvalue problem for modified pseudo-Jacobi matrices

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.113361 ◽

2021 ◽

Vol 389 ◽

pp. 113361

Author(s):

Wei-Ru Xu ◽

Natália Bebiano ◽

Guo-Liang Chen

Keyword(s):

Eigenvalue Problem ◽

Jacobi Matrices ◽

An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2021.113957 ◽

2021 ◽

pp. 113957 ◽

Cited By ~ 1

Author(s):

Wei-Ru Xu ◽

Natália Bebiano ◽

Guo-Liang Chen

Keyword(s):

Eigenvalue Problem ◽

Jacobi Matrices ◽

Inverse eigenvalue problem for pseudo-symmetric Jacobi matrices with two spectra

Linear and Multilinear Algebra ◽

10.1080/03081087.2017.1322032 ◽

2017 ◽

Vol 66 (4) ◽

pp. 759-768

Author(s):

Hanif Mirzaei

Keyword(s):

Eigenvalue Problem ◽

Jacobi Matrices ◽

A map of sufficient conditions for the real nonnegative inverse eigenvalue problem

Linear Algebra and its Applications ◽

10.1016/j.laa.2007.05.046 ◽

2007 ◽

Vol 426 (2-3) ◽

pp. 690-705 ◽

Cited By ~ 16

Author(s):

Carlos Marijuán ◽

Miriam Pisonero ◽

Ricardo L. Soto

Keyword(s):

Eigenvalue Problem ◽

Sufficient Conditions ◽

The Real ◽

A Jacobi matrix inverse eigenvalue problem with mixed data

Linear Algebra and its Applications ◽

10.1016/j.laa.2013.07.032 ◽

2013 ◽

Vol 439 (10) ◽

pp. 2774-2783 ◽

Cited By ~ 5

Author(s):

Ying Wei

Keyword(s):

Eigenvalue Problem ◽

Jacobi Matrix ◽

Mixed Data ◽

Matrix Inverse ◽

Sufficient conditions for the solvability of an algebraic inverse eigenvalue problem

Linear Algebra and its Applications ◽

10.1016/0024-3795(93)00225-o ◽

1995 ◽

Vol 221 ◽

pp. 117-129 ◽

Cited By ~ 7

Author(s):

Luoluo Li

Keyword(s):

Eigenvalue Problem ◽

Sufficient Conditions ◽

A divide and conquer algorithm on the double dimensional inverse eigenvalue problem for Jacobi matrices

Applied Mathematics and Computation ◽

10.1016/j.amc.2012.10.013 ◽

2012 ◽

Vol 219 (8) ◽

pp. 3840-3846 ◽

Cited By ~ 2

Author(s):

Xiaoqian Wu

Keyword(s):

Eigenvalue Problem ◽

Divide And Conquer ◽

Jacobi Matrices ◽

Divide And Conquer Algorithm ◽

Inverse eigenvalue problem for Jacobi matrix and nonnegative matrices

Asian-European Journal of Mathematics ◽

10.1142/s179355712250098x ◽

2021 ◽

pp. 2250098

Author(s):

Somayeh Zangoei Zadeh ◽

Azim Rivaz

Keyword(s):

Eigenvalue Problem ◽

Jacobi Matrix ◽

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.

Hochstadt inverse eigenvalue problem for Jacobi matrices

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2017.05.014 ◽

2017 ◽

Vol 455 (1) ◽

pp. 439-451 ◽

Cited By ~ 2

Author(s):

P.A. Cojuhari ◽

L.P. Nizhnik

Keyword(s):

Eigenvalue Problem ◽

Jacobi Matrices ◽

Submatrix Constrained Inverse Eigenvalue Problem involving Generalised Centrohermitian Matrices in Vibrating Structural Model Correction

East Asian Journal on Applied Mathematics ◽

10.4208/eajam.200715.181115a ◽

2016 ◽

Vol 6 (1) ◽

pp. 42-59 ◽

Cited By ~ 3

Author(s):

Wei-Ru Xu ◽

Guo-Liang Chen

Keyword(s):

Eigenvalue Problem ◽

Structural Model ◽

Sufficient Conditions ◽

Approximation Problem ◽

Frobenius Norm ◽

Structured Matrix ◽

Inverse Eigenvalue ◽

Left And Right ◽

Necessary And Sufficient

AbstractGeneralised centrohermitian and skew-centrohermitian matrices arise in a variety of applications in different fields. Based on the vibrating structure equation where M, D, G, K are given matrices with appropriate sizes and x is a column vector, we design a new vibrating structure mode. This mode can be discretised as the left and right inverse eigenvalue problem of a certain structured matrix. When the structured matrix is generalised centrohermitian, we discuss its left and right inverse eigenvalue problem with a submatrix constraint, and then get necessary and sufficient conditions such that the problem is solvable. A general representation of the solutions is presented, and an analytical expression for the solution of the optimal approximation problem in the Frobenius norm is obtained. Finally, the corresponding algorithm to compute the unique optimal approximate solution is presented, and we provide an illustrative numerical example.