Geodesic
Inverse eigenvalue problem of cell matrices
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 1015-1027
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We consider the problem of reconstructing an $n \times n$ cell matrix $D(\vec {x})$ constructed from a vector $\vec {x} = (x_{1}, x_{2},\dots , x_{n})$ of positive real numbers, from a given set of spectral data. In addition, we show that the spectra of cell matrices $D(\vec {x})$ and $D(\pi (\vec {x}))$ are the same for every permutation $\pi \in S_{n}$.
We consider the problem of reconstructing an $n \times n$ cell matrix $D(\vec {x})$ constructed from a vector $\vec {x} = (x_{1}, x_{2},\dots , x_{n})$ of positive real numbers, from a given set of spectral data. In addition, we show that the spectra of cell matrices $D(\vec {x})$ and $D(\pi (\vec {x}))$ are the same for every permutation $\pi \in S_{n}$.
DOI : 10.21136/CMJ.2019.0579-17
Classification : 15B05, 15B10, 15B48, 35P20, 35P30
Keywords: cell matrix; inverse eigenvalue problem; Euclidean distance matrix 
@article{10_21136_CMJ_2019_0579_17,
     author = {Khim, Sreyaun and Rodtes, Kijti},
     title = {Inverse eigenvalue problem of cell matrices},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1015--1027},
     year = {2019},
     volume = {69},
     number = {4},
     doi = {10.21136/CMJ.2019.0579-17},
     mrnumber = {4039616},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0579-17/}
}
TY  - JOUR
AU  - Khim, Sreyaun
AU  - Rodtes, Kijti
TI  - Inverse eigenvalue problem of cell matrices
JO  - Czechoslovak Mathematical Journal
PY  - 2019
SP  - 1015
EP  - 1027
VL  - 69
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0579-17/
DO  - 10.21136/CMJ.2019.0579-17
LA  - en
ID  - 10_21136_CMJ_2019_0579_17
ER  - 
%0 Journal Article
%A Khim, Sreyaun
%A Rodtes, Kijti
%T Inverse eigenvalue problem of cell matrices
%J Czechoslovak Mathematical Journal
%D 2019
%P 1015-1027
%V 69
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0579-17/
%R 10.21136/CMJ.2019.0579-17
%G en
%F 10_21136_CMJ_2019_0579_17
Khim, Sreyaun; Rodtes, Kijti. Inverse eigenvalue problem of cell matrices. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 1015-1027. doi: 10.21136/CMJ.2019.0579-17

[1] Chu, M. T.: Inverse eigenvalue problems. SIAM Rev. 40 (1998), 1-39. | DOI | MR | JFM

[2] Chu, M. T., Golub, G. H.: Structured inverse eigenvalue problems. Acta Numerica 11 (2002), 1-71. | DOI | MR | JFM

[3] Gyamfi, K. B.: Solution of Inverse Eigenvalue Problem of Certain Singular Hermitian Matrices. Doctoral dissertation, Kwame Nkrumah University of Science and Technology (2012).

[4] Jaklič, G., Modic, J.: On properties of cell matrices. Appl. Math. Comput. 216 (2010), 2016-2023. | DOI | MR | JFM

[5] Kurata, H., Tarazaga, P.: The cell matrix closest to a given Euclidean distance matrix. Linear Algebra Appl. 485 (2015), 194-207. | DOI | MR | JFM

[6] Nazari, A. M., Mahdinasab, F.: Inverse eigenvalue problem of distance matrix via orthogonal matrix. Linear Algebra Appl. 450 (2014), 202-216. | DOI | MR | JFM

[7] Radwan, N.: An inverse eigenvalue problem for symmetric and normal matrices. Linear Algebra Appl. 248 (1996), 101-109. | DOI | MR | JFM

[8] Schoenberg, I. J.: Metric spaces and positive definite functions. Trans. Am. Math. Soc. 44 (1938), 522-536. | DOI | MR | JFM

[9] Tarazaga, P., Kurata, H.: On cell matrices: a class of Euclidean distance matrices. Appl. Math. Comput. 238 (2014), 468-474. | DOI | MR | JFM

[10] Wang, Z., Zhong, B.: An inverse eigenvalue problem for Jacobi matrices. Math. Probl. Eng. 2011 (2011), Article ID 571781, 11 pages. | DOI | MR | JFM

Cité par Sources :