Geodesic
A simple derivation of the eigenvalues of a tridiagonal matrix arising in biogeography
Qassem M. Al-Hassan1 ; Mowaffaq Hajja2
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.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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
Mots-clés : 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 
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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. https://geodesic-test.mathdoc.fr/articles/10.4064/am42-1-3/

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