Inverse eigenproblems of real symmetric doubly arrowhead matrices.

We consider two inverse eigenproblems for a real symmetric doubly arrowhead matrix An(q), which consist of constructing An(q) from two special kinds of spectra information. These problems were introduced in [11], where the principal results are sufficient conditions for both problems to have a real solution. In this paper, we improve such conditions, in the sense that one of the given conditions implies the rest. The results are constructive and generate one numerical procedure to construct the solution matrix An(q). [ABSTRACT FROM AUTHOR]