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arXiv · 2103.03185

Sensitivity and computation of a defective eigenvalue

Zhonggang Zeng
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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.

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Zhonggang Zeng. 2021-03-04. Sensitivity and computation of a defective eigenvalue. https://doi.org/10.1137/15m1016266

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