Counting eigenvalues in domains of the complex field
Numerical Analysis
2012-03-05 v2
Abstract
A procedure for counting the number of eigenvalues of a matrix in a region surrounded by a closed curve is presented. It is based on the application of the residual theorem. The quadrature is performed by evaluating the principal argument of the logarithm of a function. A strategy is proposed for selecting a path length that insures that the same branch of the logarithm is followed during the integration. Numerical tests are reported for matrices obtained from conventional matrix test sets.
Cite
@article{arxiv.1110.4797,
title = {Counting eigenvalues in domains of the complex field},
author = {Emmanuel R. Kamgnia and Bernard Philippe},
journal= {arXiv preprint arXiv:1110.4797},
year = {2012}
}
Comments
21 pages