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dc.contributor.advisorSzyld, Daniel
dc.creatorDu, Xiuhong
dc.date.accessioned2020-11-05T16:09:42Z
dc.date.available2020-11-05T16:09:42Z
dc.date.issued2008
dc.identifier.other864884509
dc.identifier.urihttp://hdl.handle.net/20.500.12613/3675
dc.description.abstractThe GMRES method is a widely used iterative method for solving the linear systems, of the form Ax = b, especially for the solution of discretized partial differential equations. With an appropriate preconditioner, the solution of the linear system Ax = b can be achieved with less computational effort. Additive Schwarz Preconditioners have two good properties. First, they are easily parallelizable, since several smaller linear systems need to be solved: one system for each of the sub-domains, usually corresponding to the restriction of the differential operator to that subdomain. These are called local problems. Second, if a coarse problem is introduced, they are optimal in the sense that bounds on the convergence rate of the preconditioned iterative method are independent (or slowly dependent) on the finite element mesh size and the number of subproblems. We study certain cases where the same optimality can be obtained without a coarse grid correction. In another part of this thesis we consider inexact GMRES when applied to singular (or nearly singular) linear systems. This applies when instead of matrix-vector products with A, one uses A = A+E for some error matrix E which usually changes from one iteration to the next. Following a similar study by Simoncini and Szyld (2003) for nonsingular systems, we prescribe how to relax the exactness of the matrixvector product and still achieve the desired convergence. In addition, similar criteria is given to guarantee that the computed residual with the inexact method is close to the true residual. Furthermore, we give a new computable criteria to determine the inexactness of matrix-vector product using in inexact CG, and applied it onto control problems governed by parabolic partial differential equations.
dc.format.extent100 pages
dc.language.isoeng
dc.publisherTemple University. Libraries
dc.relation.ispartofTheses and Dissertations
dc.rightsIN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available.
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectMathematics
dc.subjectPreconditioner
dc.subjectGmres
dc.subjectCg
dc.subjectInexact
dc.titleAdditive Schwarz Preconditioned GMRES, Inexact Krylov Subspace Methods, and Applications of Inexact CG
dc.typeText
dc.type.genreThesis/Dissertation
dc.contributor.committeememberDatskovsky, Boris Abramovich
dc.contributor.committeememberGrabovsky, Yury
dc.contributor.committeememberShi, Yuan
dc.description.departmentMathematics
dc.relation.doihttp://dx.doi.org/10.34944/dspace/3657
dc.ada.noteFor Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
dc.description.degreePh.D.
refterms.dateFOA2020-11-05T16:09:42Z


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