Sensitivity and Computation of a Defective Eigenvalue

4 A defective eigenvalues is well documented to be hypersensitive to data pertur5 bations and round-off errors, making it a formidable challenge in numerical computa6 tion particularly when the matrix is known through approximate data. This paper 7 establishes a finitely bounded sensitivity of a defective eigenvalue with respect to per8 turbations that preserve the geometric multiplicity and the smallest Jordan block size. 9 Based on this perturbation theory, numerical computation of a defective eigenvalue is 10 regularized as a well-posed least squares problem so that it can be accurately carried 11 out using floating point arithmetic even if the matrix is perturbed. 12