Geodesic
Extreme spectra realization by real symmetric tridiagonal and real symmetric arrow matrices
The electronic journal of linear algebra, Tome 22 (2011), pp. 780-795.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider the following two problems: to construct a real symmetric arrow matrix Aand to construct a real symmetric tridiagonal matrix A, from a special kind of spectral information: one eigenvalue $\lambda (j)$ of the j $\times j$ leading principal submatrix A j of A, j = 1, 2, . . . , n; and one eigenpair $(\lambda (n) , x )$ of A. Here we give a solution to the first problem, introduced in [J. Peng, X.Y. Hu, and L. Zhang. Two inverse eigenvalue problems for a special kind of matrices. Linear Algebra Appl., 416:336-347, 2006.]. In particular, for both problems to have a solution, we give a necessary and sufficient condition in the first case, and a sufficient condition in the second one. In both cases, we also give sufficient conditions in order that the constructed matrices be nonnegative. Our results are constructive and they generate algorithmic procedures to construct such matrices.
Classification : 65F15, 65F18, 15A18
Keywords: real symmetric tridiagonal matrices, real symmetric arrow matrices, eigenproblem 
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     author = {Pickmann, Hubert and Egana, Juan C. and Soto, Ricardo L.},
     title = {Extreme spectra realization by real symmetric tridiagonal and real symmetric arrow matrices},
     journal = {The electronic journal of linear algebra},
     pages = {780--795},
     publisher = {mathdoc},
     volume = {22},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2011__22__a25/}
}
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Pickmann, Hubert; Egana, Juan C.; Soto, Ricardo L. Extreme spectra realization by real symmetric tridiagonal and real symmetric arrow matrices. The electronic journal of linear algebra, Tome 22 (2011), pp. 780-795. http://geodesic.mathdoc.fr/item/ELA_2011__22__a25/