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ELA

TWO INVERSE EIGENPROBLEMS FOR SYMMETRIC DOUBLY

ARROW MATRICES

∗

HUBERT PICKMANN†, JUAN C. EGA ˜NA†, ANDRICARDO L. SOTO†

Abstract. In this paper, the problem of constructing a real symmetric doubly arrow matrix

Afrom two special kinds of spectral information is considered. The first kind is the minimal and maximal eigenvalues of all leading principal submatrices ofA, and the second kind is one eigenvalue of each leading principal submatrix of Atogether with one eigenpair of A. Sufficient conditions for both eigenproblems to have a solution and sufficient conditions for both eigenproblems have a nonnegative solution are given in this paper. The results are constructive in the sense that they generate algorithmic procedures to compute the solution matrix.

Key words. Symmetric doubly arrow matrices, Inverse eigenproblem.

AMS subject classifications.65F15, 65F18, 15A18.

∗Received by the editors October 29, 2008. Accepted for publication October 14, 2009. Handling

Editor: Daniel Szyld.

†Departamentode Matem´aticas, Universidad Cat´olica del Norte, Antofagasta, Casilla 1280, Chile

([email protected], [email protected] and [email protected]). Supported by Fondecyt 1085125 and Project DGIP-UCN, Chile.

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 18, pp. 700-718, November 2009

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