Asymptotics of Large Eigenvalues for a Class of Band Matrices
نویسندگان
چکیده
We investigate the asymptotic behaviour of large eigenvalues for a class of finite difference self-adjoint operators with compact resolvent in l2.
منابع مشابه
A mathematically simple method based on denition for computing eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices
In this paper, a fundamentally new method, based on the denition, 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 th...
متن کاملProperties of matrices with numerical ranges in a sector
Let $(A)$ be a complex $(ntimes n)$ matrix and assume that the numerical range of $(A)$ lies in the set of a sector of half angle $(alpha)$ denoted by $(S_{alpha})$. We prove the numerical ranges of the conjugate, inverse and Schur complement of any order of $(A)$ are in the same $(S_{alpha})$.The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product, star-congruen...
متن کاملSmallest Eigenvalues of Hankel Matrices for Exponential Weights
We obtain the rate of decay of the smallest eigenvalue of the Hankel matrices R I t j+kW 2 (t) dt n j;k=0 for a general class of even exponential weights W 2 = exp ( 2Q) on an interval I. More precise asymptotics for more special weights have been obtained by many authors. Remark 1 Running Title: Smallest Eigenvalues of Hankel Matrices
متن کاملAsymptotics of individual eigenvalues of a class of large Hessenberg Toeplitz matrices
We study the asymptotic behavior of individual eigenvalues of the n × n truncations of certain infinite Hessenberg Toeplitz matrices as n goes to infinity. The generating function of the Toeplitz matrices is supposed to be of the form a(t) = t−1(1−t)αf(t) (t ∈ T), where α is a positive real number but not an integer and f is a smooth function in H∞. The classes of generating functions considere...
متن کاملTrace formula and Spectral Riemann Surfaces for a class of tri-diagonal matrices
For tri-diagonal matrices arising in the simplified Jaynes– Cummings model, we give an asymptotics of the eigenvalues, prove a trace formula and show that the Spectral Riemann Surface is irreducible.
متن کامل