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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 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]

We consider the following inverse extreme eigenvalue problem: given the real numbers {λ1j,λjj}j=1n and the real vector x(n)=x1,x2,...,xn, to construct a nonsymmetric tridiagonal matrix and a nonsymmetric arrow matrix such that {λ1j,λjj}j=1n are the minimal and the maximal eigenvalues of each one of their leading principal submatrices, and x(n),λn(n) is an eigenpair of the matrix. We give sufficient conditions for the existence of such matrices. Moreover our results generate an algorithmic procedure to compute a unique solution matrix. [ABSTRACT FROM AUTHOR]

In this paper, sufficient conditions for the existence and construction of nonnegative matrices with prescribed elementary divisors for a list of complex numbers with nonnegative real part are obtained, and the corresponding nonnegative matrices are constructed. In addition, results of how to perturb complex eigenvalues of a nonnegative matrix while keeping its elementary divisors and its nonnegativity are derived. [ABSTRACT FROM AUTHOR]