Date of Award

1-1-2017

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (ii, v, 70 pages)

Dissertation/Thesis Chair

Charles Micchelli

Committee Members

Karyn Reinhold, Yiming Ying

Keywords

Block, Matrix, norm, Pseudospectrum, singularity, Structures, Spectral theory (Mathematics), Matrices, Toeplitz matrices, Eigenvalues, Hankel operators

Subject Categories

Physical Sciences and Mathematics

Abstract

The study of pseudospectra Λε(A) dates back to the 1980s when it became an important analytical and graphical alternative for investigating non-normal matrices and operators. The interest in pseudospectra was further stimulated in the 1990s by the increasing avail- ability of numerical software such as Matlab, Eigtool and Seigtool. The main reason for the importance of pseudospectra is that eigenvalue analysis of non-self-adjoint operators can be misleading, which is most easily seen by looking at the 2-norm pseudospectra of non- normal matrices whose eigenvectors are not orthogonal. Many of the advances in the field are due to interactions between pure and applied mathematicians, and numerical analysts, and greatly driven by numerical experiments. The study of pseudospectra is motivated by a huge number of applications in mathematics and many applied fields.

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