An inverse eigenvalue problem approach to system design is considered. The Cayley-Hamilton theorem is developed for the general case involving the generalized eigenvalue vibration problem. Since many solutions exist for a desired frequency spectrum, a discussion of the required design information and suggestions for including structural constraints are given. An algorithm for solving the invers...

Let T be a tree and let x0 be a vertex of T . T is called a superstar with central vertex x0 if T − x0 is a union of paths. The General Inverse Eigenvalue Problem for certain trees is partially answered. Using this description, some superstars are presented for which the problem of ordered multiplicity lists and the Inverse Eigenvalue Problem are not equivalent.

In this paper, we consider the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M,C, and K of size n× n, with (M,C,K) / = 0, so that the quadratic matrix polynomial Q(λ) = λ2M + λC +K has m (n < m 2n) prescribed eigenpairs. It is shown that, for almost all prescribed eigenpairs, the QIEP has a solution with M nonsingular if m < m∗, and has only solutions with ...

In this paper we study the inverse eigenvalue problem for symmetric special matrices and introduce sufficient conditions for obtaining nonnegative matrices. We get the HROU algorithm from [1] and introduce some extension of this algorithm. If we have some eigenvectors and associated eigenvalues of a matrix, then by this extension we can find the symmetric matrix that its eigenvalue and eigenvec...

We show that a unitary upper Hessenberg matrix with positive subdiago-nal elements is uniquely determined by its eigenvalues and the eigenvalues of a modiied principal submatrix. This provides an analog of a well-known result for Jacobi matrices.

The estimation of the frequencies of sinusoids in noise is a very common problem. This paper addresses the estimation of sinusoids in a low SNR environment. This sinusoidal frequency estimation problem can be used to nd the carrier frequencies and baud rates of communication waveforms after some appropriate nonlinearity. If the underlying signal model is sinusoids in white Gaussian noise and we...

The detailed spectral structure of symmetric, algebraic, quadratic eigenvalue problems has been developed recently. In this paper we take advantage of these canonical forms to provide a detailed analysis of inverse problems of the form: construct the coefficient matrices from the spectral data including the classical eigenvalue/eigenvector data and sign characteristics for the real eigenvalues....