Distance matrices, nonnormality and pseudospectra
G. Tsiroyiannis, G. Tsachtsiris, C. Bekas, E. Kokiopoulou and
E. Gallopoulos
University of Patras, Greece
Abstract
The e
pseudospectrum of a matrix,
defined for example as
L_{e} (A) =
{z: z Î L(A+E)
for some E Î C^{n x n}
with  E  £
e} 

where L(A) denotes the spectrum of A, is acknowledged
to be a powerful mechanism for studying the sensitivity of eigenvalues as well as for
investigating the behavior of nonnormal matrices and operators. See, for example, the Oxford
Pseudospectra
Gateway for a wealth of information and references to the topic.
In this contribution we consider the case of
distance matrices that originate in the course of methods
used in computational electromagnetics and study their properties. We are
particularly interested in ways to quantify the sensitivity based
on information obtained from the pseudospectra. We consider novel
algorithms that use such measures to construct nonnormal
distance matrices with varying levels of sensitivity.