Isospectral flows and the inverse eigenvalue problem for 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.

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

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 a Newton Method for the Inverse Toeplitz Eigenvalue Problem

Iterative methods for inverse eigenvalue problems involve simultaneous approximation of the matrix being sought and its eigenvectors This paper revisits one such method for the inverse Toeplitz eigenvalue problems by exploring the eigenstructure of centrosymmetric matrices All itera tions are now taking place on a much smaller subspace One immediate consequence is that the size of the problem i...