  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.
