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dc.contributor.authorAksoylu, Burak
dc.contributor.authorUnlu, Zuhal
dc.date.accessioned2019-07-04T14:19:40Z
dc.date.available2019-07-04T14:19:40Z
dc.date.issued2014-03
dc.identifier.citationAksoylu, B., & Unlu, Z. (2014). Conditioning analysis of nonlocal integral operators in fractional Sobolev spaces. SIAM Journal on Numerical Analysis, 52(2), 653-677.en_US
dc.identifier.issn0036-1429
dc.identifier.urihttps://doi.org/10.1137/13092407X
dc.identifier.urihttp://hdl.handle.net/20.500.11851/1652
dc.description.abstractWe study the conditioning of nonlocal integral operators with singular and integrable kernels in fractional Sobolev spaces. These operators are used, for instance, in peridynamics formulation and nonlocal diffusion. In one dimension (1D), we present sharp quantification of the extremal eigenvalues in all three parameters: size of nonlocality, mesh size, and regularity of the fractional Sobolev space. We accomplish sharpness both rigorously and numerically. For the minimal eigenvalue, we obtain sharpness analytically by using a nonlocal characterization of Sobolev spaces. We verify this estimate by exploiting the Toeplitz property of the stiffness matrix. However, the analytical approach fails to give sharp quantification of the maximal eigenvalue. Hence, in 1D, we take an algebraic approach by directly working with the stiffness matrix entries, which have complicated expressions due to all three parameters. We systematically characterize the nonzero entries and dramatically simplify their expressions by using convenient algebra. We establish the zero row sum property of the stiffness matrix and negativity of the off-diagonal entries. Eventually, we arrive at sharpness through the use of the Gerschgorin circle theorem.en_US
dc.language.isoengen_US
dc.publisherSociety for Industrial and Applied Mathematics Publicationsen_US
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectCondition numberen_US
dc.subject Nonlocal operatorsen_US
dc.subject Peridynamicsen_US
dc.subject Nonlocal diffusionen_US
dc.subject Toeplitz matrixen_US
dc.subject The Gerschgorin circle theoremen_US
dc.subject Preconditioningen_US
dc.titleConditioning analysis of nonlocal integral operators in fractional Sobolev spacesen_US
dc.typearticleen_US
dc.relation.journalSIAM Journal on Numerical Analysisen_US
dc.contributor.departmentTOBB ETU, Faculty of Science and Literature, Department of Mathematicsen_US
dc.contributor.departmentTOBB ETÜ, Fen Edebiyat Fakültesi, Matematik Bölümütr_TR
dc.identifier.volume52
dc.identifier.issue2
dc.identifier.startpage653
dc.identifier.endpage677
dc.relation.tubitakinfo:eu-repo/grantAgreement/TÜBİTAK/TBAG/112T240en_US
dc.relation.tubitakinfo:eu-repo/grantAgreement/TÜBİTAK/MAG/112M891en_US
dc.relation.ecEuropean Union Marie Curie Career Integration [293978]en_US
dc.contributor.orcidhttps://orcid.org/0000-0002-7244-3340
dc.identifier.wosWOS:000335818000004
dc.identifier.scopus2-s2.0-84902581457
dc.contributor.tobbetuauthorAksoylu, Burak
dc.contributor.YOKid29230
dc.identifier.doi10.1137/13092407X
dc.contributor.wosresearcherIDC-4948-2016
dc.contributor.ScopusAuthorID23979376500
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıtr_TR
dc.relation.internationalNational Science Foundation DMS [1016190]en_US


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