Date Available
7-27-2013
Year of Publication
2013
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
Mathematics
First Advisor
Dr. Qiang Ye
Abstract
Diagonally dominant matrices arise in many applications. In this work, we exploit the structure of diagonally dominant matrices to provide sharp entrywise relative perturbation bounds. We first generalize the results of Dopico and Koev to provide relative perturbation bounds for the LDU factorization with a well conditioned L factor. We then establish relative perturbation bounds for the inverse that are entrywise and independent of the condition number. This allows us to also present relative perturbation bounds for the linear system Ax=b that are independent of the condition number. Lastly, we continue the work of Ye to provide relative perturbation bounds for the eigenvalues of symmetric indefinite matrices and non-symmetric matrices.
Recommended Citation
Dailey, Megan, "RELATIVE PERTURBATION THEORY FOR DIAGONALLY DOMINANT MATRICES" (2013). Theses and Dissertations--Mathematics. 11.
https://uknowledge.uky.edu/math_etds/11
