Sensitivity and computation of a defective eigenvalue
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.
SIAM Journal on Matrix Analysis and Applications
Zeng, Zhonggang, "Sensitivity and computation of a defective eigenvalue" (2016). Mathematics Faculty Publications. 6.