## Publication: Inexact and Nonlinear Extensions of the FEAST Eigenvalue Algorithm

 dc.contributor.advisor Eric Polizzi dc.contributor.author Gavin, Brendan E dc.contributor.department University of Massachusetts Amherst dc.date 2024-03-27T18:25:43.000 dc.date.accessioned 2024-04-26T15:26:19Z dc.date.available 2024-04-26T15:26:19Z dc.date.submitted September dc.date.submitted 2018 dc.description.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. dc.description.degree Doctor of Philosophy (PhD) dc.description.department Electrical and Computer Engineering dc.identifier.doi https://doi.org/10.7275/12360224 dc.identifier.orcid N/A dc.identifier.uri https://hdl.handle.net/20.500.14394/17549 dc.relation.url https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=2385&context=dissertations_2&unstamped=1 dc.source.status published dc.subject eigenvalue problem dc.subject linear algebra dc.subject contour integral dc.subject FEAST dc.subject algorithm dc.subject krylov dc.subject Numerical Analysis and Computation dc.subject Numerical Analysis and Scientific Computing dc.title Inexact and Nonlinear Extensions of the FEAST Eigenvalue Algorithm dc.type openaccess dc.type article dc.type dissertation digcom.contributor.author isAuthorOfPublication|email:brendanedwardgavin@gmail.com|institution:University of Massachusetts Amherst|Gavin, Brendan E digcom.identifier dissertations_2/1341 digcom.identifier.contextkey 12360224 digcom.identifier.submissionpath dissertations_2/1341 dspace.entity.type Publication
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