Algorithms for Computing the Optimal Geršgorin-Type Localizations

Algorithms for Computing the Optimal Geršgorin-Type Localizations

There are numerous ways to localize eigenvalues. One of the best known results is that the spectrum of a given matrix ACn,n is a subset of a union of discs centered at diagonal elements whose radii equal to the sum of the absolute values of the off-diagonal elements of a corresponding row in the mat...

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Bibliographic Details
Main Author: Milićević, Srđan
Format: Dissertation
Language:English
Published: ProQuest Dissertations & Theses 01-01-2020
Subjects:
Applied Mathematics
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Summary:There are numerous ways to localize eigenvalues. One of the best known results is that the spectrum of a given matrix ACn,n is a subset of a union of discs centered at diagonal elements whose radii equal to the sum of the absolute values of the off-diagonal elements of a corresponding row in the matrix. This result (Geršgorin's theorem, 1931) is one of the most important and elegant ways of eigenvalues localization ([63]). Among all Geršgorintype sets, the minimal Geršgorin set gives the sharpest and the most precise localization of the spectrum ([39]). In this thesis, new algorithms for computing an efficient and accurate approximation of the minimal Geršgorin set are presented.
ISBN:9798664714210