Some remarks on the inverse eigenvalue problem for real symmetric Toeplitz matrices

Some remarks on the inverse eigenvalue problem for real symmetric Toeplitz matrices

Two theorems about the solution properties of the Toeplitz Inverse Eigenvalue Problem (ToIEP) are introduced and proved. One of them is applied to make a better starting generator and the other can be used to double the number of solutions found. These applications are tested through a short Mathematica program. Also an optimisation method for solving ToIEP with global convergence property is p...

Some results on the symmetric doubly stochastic inverse eigenvalue problem

‎The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$‎, ‎to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$‎. ‎If there exists an $ntimes n$ symmetric doubly stochastic ...

Numerical Solution of the Inverse Eigenvalue Problem for Real Symmetric Toeplitz Matrices

On the nonnegative inverse eigenvalue problem of traditional matrices

In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.

On the Inverse Eigenvalue Problem for Real Circulant Matrices

The necessary condition for eigenvalue values of a circulant matrix is studied It is then proved that the necessary condition also su ces the existence of a circulant matrix with the prescribed eigenvalue values Introduction An n n matrix C of the form C c c cn cn c c cn cn cn c cn c c cn c is called a circulant matrix As each row of a circulant matrix is just the previous row cycled forward on...