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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]

In this paper, we give sufficient conditions for the construction of periodic and generalized periodic Jacobi matrices from particular spectral data. For the construction of a periodic Jacobi matrix, the smallest and largest eigenvalues of all its leading principal submatrices, and a prescribed entry are required. For the case of the generalized periodic Jacobi matrix, an eigenvector associated with the largest eigenvalue is additionally considered. The results obtained provide algorithmic procedures that are illustrated in some numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we give sufficient conditions for the construction of certain symmetric and nonsymmetric pentadiagonal matrices from particular spectral information. The construction of the symmetric pentadiagonal matrix considers the extreme eigenvalues of its leading principal submatrices and a prescribed entry, and the construction of the nonsymmetric pentadiagonal matrix also considers an eigenvector and two prescribed entries. [ABSTRACT FROM AUTHOR]

This article considers two inverse eigenvalue problems for Lefkovitch and doubly Lefkovitch matrices. The problems consist of constructing these matrices from the maximal eigenvalues of all its leading principal submatrices, eigenvectors associated with some of these eigenvalues, and some diagonal entries. We give sufficient conditions for the existence of such matrices. In particular, when the matrices have constant diagonal entries. In addition, we provide numerical examples to show the results obtained. [ABSTRACT FROM AUTHOR]

In this paper, we deal with Leslie and doubly Leslie matrices of order n. In particular, with the companion and doubly companion matrices. We study three inverse eigenvalues problems which consist of constructing these matrices from the maximal eigenvalues of its all leading principal submatrices. For Leslie and doubly companion matrices, an eigenvector associated with the maximal eigenvalue of the matrix is additionally considered, and for the doubly Leslie matrix also an eigenvector associated with the maximal eigenvalue of leading principal submatrix of order n − 1 is required. We give necessary and sufficient conditions for the existence of a Leslie matrix and a companion matrix, and sufficient conditions for the existence of a doubly Leslie matrix and a doubly companion matrix. Our results are constructive and generate an algorithmic procedure to construct these special kinds of matrices. [ABSTRACT FROM AUTHOR]