{"id":"https://openalex.org/W2017453755","doi":"https://doi.org/10.1137/13092407x","title":"Conditioning Analysis of Nonlocal Integral Operators in Fractional Sobolev Spaces","display_name":"Conditioning Analysis of Nonlocal Integral Operators in Fractional Sobolev Spaces","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2017453755","doi":"https://doi.org/10.1137/13092407x","mag":"2017453755"},"language":"en","primary_location":{"id":"doi:10.1137/13092407x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/13092407x","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078880740","display_name":"Burak Aksoylu","orcid":"https://orcid.org/0000-0002-7244-3340"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Burak Aksoylu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5023762355","display_name":"Zuhal Unlu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zuhal Unlu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078880740"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.5008,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.97976485,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"52","issue":"2","first_page":"653","last_page":"677"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9818999767303467,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8674786686897278},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.7864875793457031},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6532571911811829},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5327093005180359},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5234619975090027},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.49174049496650696},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.43890121579170227},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.4301917552947998},{"id":"https://openalex.org/keywords/sobolev-inequality","display_name":"Sobolev inequality","score":0.41928568482398987},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38584238290786743},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13395172357559204}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8674786686897278},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.7864875793457031},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6532571911811829},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5327093005180359},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5234619975090027},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.49174049496650696},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.43890121579170227},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4301917552947998},{"id":"https://openalex.org/C185644265","wikidata":"https://www.wikidata.org/wiki/Q3711848","display_name":"Sobolev inequality","level":3,"score":0.41928568482398987},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38584238290786743},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13395172357559204},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/13092407x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/13092407x","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W200978043","https://openalex.org/W1569512514","https://openalex.org/W1578503622","https://openalex.org/W1968296083","https://openalex.org/W1969333017","https://openalex.org/W1970969242","https://openalex.org/W1973127220","https://openalex.org/W1974725498","https://openalex.org/W1977278511","https://openalex.org/W1977452126","https://openalex.org/W1977835576","https://openalex.org/W1982427175","https://openalex.org/W1983652726","https://openalex.org/W1985849851","https://openalex.org/W1990654557","https://openalex.org/W1993193430","https://openalex.org/W1993215954","https://openalex.org/W1994183212","https://openalex.org/W2000897527","https://openalex.org/W2001730319","https://openalex.org/W2006044588","https://openalex.org/W2007393042","https://openalex.org/W2011095781","https://openalex.org/W2012828992","https://openalex.org/W2014340982","https://openalex.org/W2017537208","https://openalex.org/W2028507255","https://openalex.org/W2029529153","https://openalex.org/W2032440993","https://openalex.org/W2036587683","https://openalex.org/W2038885598","https://openalex.org/W2040495894","https://openalex.org/W2041006357","https://openalex.org/W2046571480","https://openalex.org/W2060945009","https://openalex.org/W2064845551","https://openalex.org/W2066970061","https://openalex.org/W2068276211","https://openalex.org/W2068701402","https://openalex.org/W2078050228","https://openalex.org/W2082954912","https://openalex.org/W2086186956","https://openalex.org/W2088485015","https://openalex.org/W2095653883","https://openalex.org/W2107828767","https://openalex.org/W2139045013","https://openalex.org/W2143206135","https://openalex.org/W2164158190","https://openalex.org/W2313618896","https://openalex.org/W2620978636","https://openalex.org/W4289257084"],"related_works":["https://openalex.org/W1543558945","https://openalex.org/W1973865997","https://openalex.org/W1997951687","https://openalex.org/W1975253450","https://openalex.org/W2049851965","https://openalex.org/W2317176613","https://openalex.org/W2120620275","https://openalex.org/W2322940471","https://openalex.org/W1535410608","https://openalex.org/W2087968352"],"abstract_inverted_index":{"We":[0,57,80,131,146],"study":[1],"the":[2,38,53,65,86,90,94,103,118,134,148,154,160,169,172],"conditioning":[3],"of":[4,37,46,52,77,89,102,153,159,171],"nonlocal":[5,27,75],"integral":[6],"operators":[7,18],"with":[8,117],"singular":[9],"and":[10,26,50,62,137,157],"integrable":[11],"kernels":[12],"in":[13,23,41,107],"fractional":[14,54],"Sobolev":[15,55,78],"spaces.":[16,79],"These":[17],"are":[19],"used,":[20],"for":[21],"instance,":[22],"peridynamics":[24],"formulation":[25],"diffusion.":[28],"In":[29],"one":[30],"dimension":[31],"(1D),":[32],"we":[33,68,109,164],"present":[34],"sharp":[35,100],"quantification":[36,101],"extremal":[39],"eigenvalues":[40],"all":[42,128],"three":[43,129],"parameters:":[44],"size":[45],"nonlocality,":[47],"mesh":[48],"size,":[49],"regularity":[51],"space.":[56],"accomplish":[58],"sharpness":[59,70,167],"both":[60],"rigorously":[61],"numerically.":[63],"For":[64],"minimal":[66],"eigenvalue,":[67],"obtain":[69],"analytically":[71],"by":[72,84,114,142],"using":[73,143],"a":[74],"characterization":[76],"verify":[81],"this":[82],"estimate":[83],"exploiting":[85],"Toeplitz":[87],"property":[88,152],"stiffness":[91,119,155],"matrix.":[92],"However,":[93],"analytical":[95],"approach":[96,113],"fails":[97],"to":[98,127],"give":[99],"maximal":[104],"eigenvalue.":[105],"Hence,":[106],"1D,":[108],"take":[110],"an":[111],"algebraic":[112],"directly":[115],"working":[116],"matrix":[120,156],"entries,":[121],"which":[122],"have":[123],"complicated":[124],"expressions":[125,141],"due":[126],"parameters.":[130],"systematically":[132],"characterize":[133],"nonzero":[135],"entries":[136],"dramatically":[138],"simplify":[139],"their":[140],"convenient":[144],"algebra.":[145],"establish":[147],"zero":[149],"row":[150],"sum":[151],"negativity":[158],"off-diagonal":[161],"entries.":[162],"Eventually,":[163],"arrive":[165],"at":[166],"through":[168],"use":[170],"Gerschgorin":[173],"circle":[174],"theorem.":[175]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}