Sensitivity and computation of a defective eigenvalue
Numerical Analysis
2021-03-05 v1 Numerical Analysis
Abstract
A defective eigenvalue is well documented to be hypersensitive to data perturbations and round-off? errors, making it a formidable challenge in numerical computation particularly when the matrix is known through approximate data. This paper establishes a finitely bounded sensitivity of a defective eigenvalue with respect to perturbations that preserve the geometric multiplicity and the smallest Jordan block size. Based on this perturbation theory, numerical computation of a defective eigenvalue is regularized as a well-posed least squares problem so that it can be accurately carried out using floating point arithmetic even if the matrix is perturbed.
Cite
@article{arxiv.2103.03185,
title = {Sensitivity and computation of a defective eigenvalue},
author = {Zhonggang Zeng},
journal= {arXiv preprint arXiv:2103.03185},
year = {2021}
}