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This paper studies two inverse eigenvalue problems for two kinds of acyclic matrices whose graphs are caterpillars. The spectral data of the first problem considers the minimal and maximal eigenvalues of all leading principal submatrices of the matrix. The second consists of an extremal eigenvalue of each leading principal submatrix and one eigenpair of the matrix. In the main results, we give sufficient conditions for the existence of such matrices, and their proofs provide algorithmic procedures for their construction. Finally, we present some numerical examples that illustrate the applicability of the solutions obtained. [ABSTRACT FROM AUTHOR]

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]

We present a new construction of a symmetric arrow matrix from a particular spectral information: let ɻ(n) be the minimal eigenvalue of the matrix and ɻ®, j = 1, 2,..., n the maximal eigenvalues of all leading principal submatrices of the matrix. We use such a procedure to construct a nonsymmetric arrow matrix from the same spectral information plus to an eigenvector X(n) = (x1 x2 . . ., xn, so that (X(n), ɻn(n) is an eigenpair of the matrix. Moreover, our results generate an algorithmic procedure to compute a solution matrix. [ABSTRACT FROM AUTHOR]