Geodesic
A simple derivation of the eigenvalues of a tridiagonal matrix arising in biogeography
Qassem M. Al-Hassan 1   ; Mowaffaq Hajja 2
1 Department of Mathematics Yarmouk University Irbid, Jordan
2 Department of Mathematics Yarmouk University, Irbid Jordan
Applicationes Mathematicae, Tome 42 (2015) no. 1, pp. 23-27 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

In investigating a certain optimization problem in biogeography, Simon [IEEE Trans. Evolutionary Comput. 12 (2008), 702–713] encountered a certain specially structured tridiagonal matrix and made a conjecture regarding its eigenvalues. A few years later, the validity of the conjecture was established by Igelnik and Simon [Appl. Math. Comput. 218 (2011), 195–201]. In this paper, we give another proof of this conjecture that is much shorter, almost computation-free, and does not resort to the eigenvectors of the matrix.
DOI : 10.4064/am42-1-3
Keywords: investigating certain optimization problem biogeography simon ieee trans evolutionary comput encountered certain specially structured tridiagonal matrix made conjecture regarding its eigenvalues few years later validity conjecture established igelnik simon appl math comput paper another proof conjecture much shorter almost computation free does resort eigenvectors matrix

Qassem M. Al-Hassan  1   ; Mowaffaq Hajja  2

1 Department of Mathematics Yarmouk University Irbid, Jordan
2 Department of Mathematics Yarmouk University, Irbid Jordan 
@article{10_4064_am42_1_3,
     author = {Qassem M. Al-Hassan and Mowaffaq Hajja},
     title = {A simple derivation of the eigenvalues of a tridiagonal matrix arising in biogeography},
     journal = {Applicationes Mathematicae},
     pages = {23--27},
     year = {2015},
     volume = {42},
     number = {1},
     doi = {10.4064/am42-1-3},
     zbl = {1329.15027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am42-1-3/}
}
TY  - JOUR
AU  - Qassem M. Al-Hassan
AU  - Mowaffaq Hajja
TI  - A simple derivation of the eigenvalues of a tridiagonal matrix arising in biogeography
JO  - Applicationes Mathematicae
PY  - 2015
SP  - 23
EP  - 27
VL  - 42
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am42-1-3/
DO  - 10.4064/am42-1-3
LA  - en
ID  - 10_4064_am42_1_3
ER  - 
%0 Journal Article
%A Qassem M. Al-Hassan
%A Mowaffaq Hajja
%T A simple derivation of the eigenvalues of a tridiagonal matrix arising in biogeography
%J Applicationes Mathematicae
%D 2015
%P 23-27
%V 42
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/am42-1-3/
%R 10.4064/am42-1-3
%G en
%F 10_4064_am42_1_3
Qassem M. Al-Hassan; Mowaffaq Hajja. A simple derivation of the eigenvalues of a tridiagonal matrix arising in biogeography. Applicationes Mathematicae, Tome 42 (2015) no. 1, pp. 23-27. doi: 10.4064/am42-1-3

Cité par Sources :