The method called Arnoldi is currently a very popular method to solve largescale eigenvalue problems. The general purpose of this paper is to generalize Arnoldi to the characteristic equation of a delay-differential equation (DDE), here called a delay eigenvalue problem. The DDE can equivalently be expressed with a linear infinite dimensional operator which eigenvalues are the solutions to the ...

We are concerned with the perturbation of a multiple eigenvalue μ of the Hermitian matrix A = diag(μI,A22) when it undergoes an off-diagonal perturbation E whose columns have widely varying magnitudes. When some of E’s columns are much smaller than the others, some copies of μ are much less sensitive than any existing bound suggests. We explain this phenomenon by establishing individual perturb...

In this paper, we propose a method for finding certain eigenvalues of a generalized eigenvalue problem that lie in a given domain of the complex plane. The proposed method projects the matrix pencil onto a subspace associated with the eigenvalues that are located in the domain via numerical integration. The projection produces a small pencil with Hankel matrices.

We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specified eigenvalues. We derive a singular value optimization characterization for this problem and illustrate its usefulness for two applications. First, the characterization yields a singular value formula for determining the nearest pencil whose eigenvalues lie in a...

Moments and functions of moments are powerful general tools in a vast number of fields, and particularly in the field of image signal processing. In this paper, we present a method for obtaining a set of orthogonal, noise-robust, transformation invariant and distribution sensitive moments, which we call Eigenmoments (EM). EM are obtained by performing eigen analysis in the moment space generate...