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Author ORCID Identifier
N/A
AccessType
Open Access Dissertation
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Electrical and Computer Engineering
Year Degree Awarded
2018
Month Degree Awarded
September
First Advisor
Eric Polizzi
Subject Categories
Numerical Analysis and Computation | Numerical Analysis and Scientific Computing
Abstract
Eigenvalue problems are a basic element of linear algebra that have a wide variety of applications. Common examples include determining the stability of dynamical systems, performing dimensionality reduction on large data sets, and predicting the physical properties of nanoscopic objects. Many applications require solving large dimensional eigenvalue problems, which can be very challenging when the required number of eigenvalues and eigenvectors is also large. The FEAST algorithm is a method of solving eigenvalue problems that allows one to calculate large numbers of eigenvalue/eigenvector pairs by using contour integration in the complex plane to divide the large number of desired pairs into many small groups; these small groups of eigenvalue/eigenvector pairs may then be simultaneously calculated independently of each other. This makes it possible to quickly solve eigenvalue problems that might otherwise be very difficult to solve efficiently.
The standard FEAST algorithm can only be used to solve eigenvalue problems that are linear, and whose matrices are small enough to be factorized efficiently (thus allowing linear systems of equations to be solved exactly). This limits the size and the scope of the problems to which the FEAST algorithm may be applied. This dissertation describes extensions of the standard FEAST algorithm that allow it to efficiently solve nonlinear eigenvalue problems, and eigenvalue problems whose matrices are large enough that linear systems of equations can only be solved inexactly.
DOI
https://doi.org/10.7275/12360224
Recommended Citation
Gavin, Brendan E., "Inexact and Nonlinear Extensions of the FEAST Eigenvalue Algorithm" (2018). Doctoral Dissertations. 1341.
https://doi.org/10.7275/12360224
https://scholarworks.umass.edu/dissertations_2/1341
Included in
Numerical Analysis and Computation Commons, Numerical Analysis and Scientific Computing Commons