Matrix Perturbation Theory

Survey of Componentwise Perturbation Theory

Perturbation bounds in numerical linear algebra are traditionally derived and expressed using norms. Norm bounds cannot reeect the scaling or sparsity of a problem and its perturbation, and so can be unduly weak. If the problem data and its perturbation are measured componentwise, much smaller and more revealing bounds can be obtained. A survey is given of componentwise perturbation theory in n...

Perturbation Theory for Rectangular Matrix Pencils Perturbation Theory for Rectangular Matrix Pencils

abstract The theory of eigenvalues and eigenvectors of rectangular matrix pencils is complicated by the fact that arbitrarily small perturbations of the pencil can cause them disappear. However, there are applications in which the properties of the pencil ensure the existence of eigen-values and eigenvectors. In this paper it is shown how to develop a perturbation theory for such pencils. ABSTR...

Perturbation Analysis for the Matrix Equation X − ∑

Analytic Equation of State for the Square-well Plus Sutherland Fluid from Perturbation Theory

Analytic expressions were derived for the compressibility factor and residual internal energy of the square-well plus Sutherland fluid. In this derivation, we used the second order Barker-Henderson perturbation theory based on the macroscopic compressibility approximation together with an analytical expression for radial distribution function of the reference hard sphere fluid. These properties...

A Perturbation Bound of the Drazin Inverse of a Matrix by Separation of Simple Invariant Subspaces

A constructive perturbation bound of the Drazin inverse of a square matrix is derived using a technique proposed by G. Stewart and based on perturbation theory for invariant subspaces. This is an improvement of the result published by the authors Wei and Li [Numer. Linear Algebra Appl., 10 (2003), pp. 563–575]. It is a totally new approach to developing perturbation bounds for the Drazin invers...

Boundary Reflection Matrix in Perturbative Quantum Field Theory

We study boundary reflection matrix for the quantum field theory defined on a half line using Feynman’s perturbation theory. The boundary reflection matrix can be extracted directly from the two-point correlation function. This enables us to determine the boundary reflection matrix for affine Toda field theory with the Neumann boundary condition modulo ‘a mysterious factor half’. jideog.kim@dur...