Title
Sensitivity and computation of a defective eigenvalue
Document Type
Article
Publication Date
1-1-2016
Abstract
A defective eigenvalue is well documented to be hypersensitive to data perturbations and round-oif 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.
DOI
10.1137/15M1016266
Publication Title
SIAM Journal on Matrix Analysis and Applications
Volume Number
37
Issue Number
2
First Page
798
Last Page
817
ISSN
08954798
Recommended Citation
Zeng, Zhonggang, "Sensitivity and computation of a defective eigenvalue" (2016). Mathematics Faculty Publications. 6.
https://neiudc.neiu.edu/math-pub/6