dc.contributor.author Aksoylu, Burak dc.contributor.author Unlu, Zuhal dc.date.accessioned 2019-07-04T14:19:40Z dc.date.available 2019-07-04T14:19:40Z dc.date.issued 2014-03 dc.identifier.citation Aksoylu, 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.issn 0036-1429 dc.identifier.uri https://doi.org/10.1137/13092407X dc.identifier.uri http://hdl.handle.net/20.500.11851/1652 dc.description.abstract We 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.iso eng en_US dc.publisher Society for Industrial and Applied Mathematics Publications en_US dc.rights info:eu-repo/semantics/closedAccess dc.subject Condition number en_US dc.subject Nonlocal operators en_US dc.subject Peridynamics en_US dc.subject Nonlocal diffusion en_US dc.subject Toeplitz matrix en_US dc.subject The Gerschgorin circle theorem en_US dc.subject Preconditioning en_US dc.title Conditioning analysis of nonlocal integral operators in fractional Sobolev spaces en_US dc.type article en_US dc.relation.journal SIAM Journal on Numerical Analysis en_US dc.contributor.department TOBB ETU, Faculty of Science and Literature, Department of Mathematics en_US dc.contributor.department TOBB ETÜ, Fen Edebiyat Fakültesi, Matematik Bölümü tr_TR dc.identifier.volume 52 dc.identifier.issue 2 dc.identifier.startpage 653 dc.identifier.endpage 677 dc.relation.tubitak info:eu-repo/grantAgreement/TÜBİTAK/TBAG/112T240 en_US dc.relation.tubitak info:eu-repo/grantAgreement/TÜBİTAK/MAG/112M891 en_US dc.relation.ec European Union Marie Curie Career Integration [293978] en_US dc.contributor.orcid https://orcid.org/0000-0002-7244-3340 dc.identifier.wos WOS:000335818000004 dc.identifier.scopus 2-s2.0-84902581457 dc.contributor.tobbetuauthor Aksoylu, Burak dc.contributor.YOKid 29230 dc.identifier.doi 10.1137/13092407X dc.contributor.wosresearcherID C-4948-2016 dc.contributor.ScopusAuthorID 23979376500 dc.relation.publicationcategory Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı tr_TR dc.relation.international National Science Foundation DMS [1016190] en_US
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