Locating a nearest matrix with an eigenvalue of prespecified algebraic multiplicity
نویسنده
چکیده
The Wilkinson distance of a matrix A is the two-norm of the smallest perturbation E so that A + E has a multiple eigenvalue. Malyshev derived a singular value optimization characterization for the Wilkinson distance. In this work we generalize the definition of the Wilkinson distance as the two-norm of the smallest perturbation so that the perturbed matrix has an eigenvalue of prespecified algebraic multiplicity. We provide a singular value characterization for this generalized Wilkinson distance. Then we outline a numerical technique to solve the derived singular value optimization problems. In particular the numerical technique is applicable to Malyshev’s formula to compute the Wilkinson distance as well as to retrieve a nearest matrix with a multiple eigenvalue. Mathematics Subject Classification (2000) 15A18 · 90C56 · 15A60 · 65K10
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عنوان ژورنال:
- Numerische Mathematik
دوره 118 شماره
صفحات -
تاریخ انتشار 2011