Eigenvalue bounds for matrices.
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Date
2018
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Abstract
Eigenvalues are characteristic of linear operators. Once the spectrum of a matrix is
known then its Jordan Canonical form can be determined which simplifies the un-
derstanding of the matrix. For large matrices and spectral analysis sometimes it is
only necessary to know the eigenvalues of smallest and largest absolute values. Hence we consider
various strategies of bounding the spectrum in the complex plane. Such bounds may be
numerically improved by various algorithms. The minimal and maximal eigenvalues are crucial to
determine the condition number of linear systems.
Description
Master of Science in Applied Mathematics, University of KwaZulu-Natal, Westville, 2018.