The purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of Sturm-Liouville problem with equation of the form w??=(?2f(x)?R(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in C2(a,b which has a single zero (so called turning point) at point 0x=x and R(x) is a continuously differentiable function. ...

This paper proposes an eigenvector-based method for analysis and design of hierarchical networks for multi-agent systems. We first define the concept of eigen-connection by characterizing low rank information flow between layers based on the eigenvector of lower level interconnection structures. It is shown that the resulting intergroup interconnections affect only a few eigenvalues of intercon...

The paper explores new expansions of the eigenvalues for −∆u = λρu in S with Dirichlet boundary conditions by the bilinear element (denoted Q1) and three nonconforming elements, the rotated bilinear element (denoted Qrot 1 ), the extension of Q rot 1 (denoted EQ rot 1 ) and Wilson’s elements. The expansions indicate that Q1 and Qrot 1 provide upper bounds of the eigenvalues, and that EQrot 1 an...

We consider the eigenvalue problem associated to the vibrations of a string with rapidly oscillating periodic density. In a previous paper we stated asymptotic formulas for the eigenvalues and eigenfunctions when the size of the microstructure is shorter than the wavelength of the eigenfunctions 1/ √ λ . On the other hand, it has been observed that when the size of the microstructure is of the ...

Many statistical applications require the solution of a symmetric positive definite covariance matrix, sometimes with a large number of right-hand sides of a statistical independence nature. With preconditioning, the preconditioned matrix has almost all the eigenvalues clustered within a narrow range, except for a few extreme eigenvalues deviating from the range rapidly. We derive a deflated ve...