The inverse eigenvalue problem for real symmetric Toeplitz matrices

Numerical Solution of 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...

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.

The inverse eigenvalue problem for symmetric anti-bidiagonal matrices

X iv :m at h/ 05 05 09 5v 1 [ m at h. R A ] 5 M ay 2 00 5 The inverse eigenvalue problem for symmetric anti-bidiagonal matrices Olga Holtz Department of Mathematics University of California Berkeley, California 94720 USA March 6, 2008

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 ...