Skip to Main Content
Frequently Asked Questions
Submit an ETD
Global Search Box
Need Help?
Keyword Search
Participating Institutions
Advanced Search
School Logo
Files
File List
case1181231690.pdf (476.62 KB)
ETD Abstract Container
Abstract Header
On the Field of Values of the Inverse of a Matrix
Author Info
Zachlin, Paul Francis
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=case1181231690
Abstract Details
Year and Degree
2007, Doctor of Philosophy, Case Western Reserve University, Applied Mathematics.
Abstract
This dissertation concerns the field of values of the inverse of a matrix. Techniques of approximation of this set are considered for large, sparse matrices, and applications are discussed. A new method is presented that is similar in computational cost to previous methods, but may yield better approximations in practice. Also, a new technique for finding eigenvalue inclusion regions is presented, developed from the relationship between the field of values of the inverse and the eigenvalue extraction technique known as harmonic Rayleigh-Ritz. By intersecting these eigenvalue inclusion regions, a new characterization of the spectrum of a matrix is obtained. The technique for generating these regions can be generalized by replacing the field of values with other eigenvalue inclusion sets, and this is demonstrated using the Geršgorin region of a matrix.
Committee
David Singer (Advisor)
Pages
70 p.
Keywords
matrix inverse
;
Harmonic Rayleigh-Ritz
;
inclusion regions
;
exclusion regions
;
field of values
;
numerical range
;
large sparse matrix
;
Gershgorin regions
;
Arnoldi
Recommended Citations
Refworks
EndNote
RIS
Mendeley
Citations
Zachlin, P. F. (2007).
On the Field of Values of the Inverse of a Matrix
[Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1181231690
APA Style (7th edition)
Zachlin, Paul.
On the Field of Values of the Inverse of a Matrix.
2007. Case Western Reserve University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=case1181231690.
MLA Style (8th edition)
Zachlin, Paul. "On the Field of Values of the Inverse of a Matrix." Doctoral dissertation, Case Western Reserve University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=case1181231690
Chicago Manual of Style (17th edition)
Abstract Footer
Document number:
case1181231690
Download Count:
1,376
Copyright Info
© 2007, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.