This paper explores the relationship between Toeplitz and circulant matrices. Upper and lower bounds for all eigenvalues of hermitian Toeplitz matrices are given, capitalizing on the possibility of embedding a Toeplitz matrix in a circulant, and of expressing any nn Toeplitz matrix as a sum of two matrices with known eigenvalues. The bounds can be simultaneously found using a single discrete Fo...

in this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. some examples are provided to show the accuracy and reliability of the proposed method. it is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to t...

Determination of the eigenvalues and eigenvectors of a matrix is important in many areas of science, for example in web ranking [8, 15], computer graphics and visualization [24], quantum mechanics [5], statistics [12, 20], medicine, communications, construction vibration analysis [3, 23]. One of the most important numerical methods designed to calculate the eigenvalues and eigenvectors of matri...

Ostrowski type and Brauer type theorems are derived for the left eigenvalues of quaternionic matrix. We see that the above theorems for the left eigenvalues are also true for the case of right eigenvalues, when the diagonals of quaternionic matrix are real. Some distribution theorems are given in terms of ovals of Cassini that are sharper than the Ostrowski type theorems, respectively, for the ...

In this paper, we consider the localization of generalized eigenvalues, and we discuss ways in which the Gersgorin set for generalized eigenvalues can be approximated. Earlier, Stewart proposed an approximation using a chordal metric. We will obtain here an improved approximation, and using the concept of generalized diagonal dominance, we prove that the new approximation has some of the basic ...

We give a simple, transparent, and intuitive proof that all eigenvalues of the Anderson model in the region of localization are simple. The Anderson tight binding model is given by the random Hamiltonian Hω = −∆ + Vω on l 2(Z), where ∆(x, y) = 1 if |x − y| = 1 and zero otherwise, and the random potential Vω = {Vω(x), x ∈ Z } consists of independent identically distributed random variables whose...

The classical Gershgorin theorem on localization of the eigenvalues finite matrices is extended to infinite Hille-Tamarkin matrices. Applications order entire functions
 are also discussed.

We report on numerical studies of the influence of Coulomb interactions on localization of electronic wavefunctions in a strong magnetic field. Interactions are treated in the Hartree-Fock approximation. Localization properties are studied both by evaluating participation ratios of Hartree-Fock eigenfunc-tions and by studying the boundary-condition dependence of Hartree-Fock eigenvalues. We fin...