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Structured Pseudospectra of Block Matrix Structures.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Structured Pseudospectra of Block Matrix Structures./
Author:	Ferro, Richard.
Description:	1 online resource (75 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
Contained By:	Dissertation Abstracts International78-10B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369780123

Structured Pseudospectra of Block Matrix Structures.
Ferro, Richard.

Structured Pseudospectra of Block Matrix Structures. - 1 online resource (75 pages)

Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

The study of pseudospectra Lambdaepsilon(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 availability 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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369780123Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Structured Pseudospectra of Block Matrix Structures.
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100 1 $a Ferro, Richard. $3 1180612
245 1 0 $a Structured Pseudospectra of Block Matrix Structures.
264 0 $c 2017
300 $a 1 online resource (75 pages)
336 $a text $b txt $2 rdacontent
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338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
500 $a Advisers: Charles Micchelli; Jani Virtanen.
502 $a Thesis (Ph.D.) $c State University of New York at Albany $d 2017.
504 $a Includes bibliographical references
520 $a The study of pseudospectra Lambdaepsilon(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 availability 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.
520 $a Given a matrix A of certain structure, such as symmetric, Toeplitz or Hankel, it is natural to consider only perturbations DeltaA of the same structure as A when computing the eigenvalues of A + DeltaA with ||DeltaA|| < epsilon. This leads to the concept of structured epsilon-pseudospectra Lambdaepsilonstruct(A). While the theory of pseudospectra is well developed with vast literature, much less is known about structured pseudospectra of matrices, especially of matrices that possess block structures. Motivation for structured pseudospectra comes from applications, such as floating-point error analysis; situations where the entries are affected by experimental uncertainty; backward error analysis, numerical algorithms and other spectral problems in linear algebra; problems in control theory; and stability theory for dynamical systems.
520 $a In many situations it is important to know whether the structured and unstructured pseudospectra coincide. Previously it was shown that for many mainstream structures, Lambdaepsilon(A) = Lambdaepsilonstruct(A) in the scalar case. No results of this type were known for block matrices. The main results of this thesis show that for many block structures the equality remains true. Part of the approach is based on the use of (structured) distance to singularity, which is also further developed in this thesis. The block structures that are studied are so-called double structures; that is, the entries of the given matrix are of the same structure as the block matrix. We conjecture that our results remain true for most standard block structures such as block Toeplitz matrices and block Hankel matrices. We also suggest that further numerical study is needed to better understand the behavior of block matrices; in particular, a tool similar to Seigtool would be useful for block structures. It would also be interesting to know whether the equivalence of the structured and unstructured pseudospectra remains true for other norms than the spectral norm.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a State University of New York at Albany. $b Mathematics. $3 1180613
773 0 $t Dissertation Abstracts International $g 78-10B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10258453 $z click for full text (PQDT)