{"id":"https://openalex.org/W2009926490","doi":"https://doi.org/10.1137/120890600","title":"Bounds on Eigenvalues of Matrices Arising from Interior-Point Methods","display_name":"Bounds on Eigenvalues of Matrices Arising from Interior-Point Methods","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2009926490","doi":"https://doi.org/10.1137/120890600","mag":"2009926490"},"language":"en","primary_location":{"id":"doi:10.1137/120890600","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120890600","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","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/A5070728305","display_name":"Chen Greif","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Chen Greif","raw_affiliation_strings":["University of British Columbia"],"affiliations":[{"raw_affiliation_string":"University of British Columbia","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087926605","display_name":"Erin Moulding","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Erin Moulding","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5027758717","display_name":"Dominique Orban","orcid":"https://orcid.org/0000-0002-8017-7687"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dominique Orban","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070728305"],"corresponding_institution_ids":["https://openalex.org/I141945490"],"apc_list":null,"apc_paid":null,"fwci":5.889,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.96429879,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"24","issue":"1","first_page":"49","last_page":"83"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7961385250091553},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.7689242362976074},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7312593460083008},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.6993927955627441},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6306036114692688},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.6118015050888062},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4654484689235687},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.46323153376579285},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45183712244033813},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4494926929473877},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4375399649143219},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.4303804337978363},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.41482940316200256},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40037107467651367},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2754817306995392},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15641862154006958}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7961385250091553},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.7689242362976074},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7312593460083008},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.6993927955627441},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6306036114692688},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.6118015050888062},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4654484689235687},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.46323153376579285},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45183712244033813},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4494926929473877},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4375399649143219},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.4303804337978363},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.41482940316200256},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40037107467651367},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2754817306995392},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15641862154006958},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120890600","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120890600","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"},{"id":"pmh:oai:publications.polymtl.ca:12276","is_oa":false,"landing_page_url":"https://publications.polymtl.ca/12276/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401013","display_name":"PolyPublie (\u00c9cole Polytechnique de Montr\u00e9al)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45683168","host_organization_name":"Polytechnique Montr\u00e9al","host_organization_lineage":["https://openalex.org/I45683168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article de revue"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1518039036","https://openalex.org/W1967810262","https://openalex.org/W1971536112","https://openalex.org/W1978115826","https://openalex.org/W1978554456","https://openalex.org/W1979359234","https://openalex.org/W1986225835","https://openalex.org/W1991682620","https://openalex.org/W1999331305","https://openalex.org/W2010761584","https://openalex.org/W2013945499","https://openalex.org/W2017666390","https://openalex.org/W2019744552","https://openalex.org/W2030723843","https://openalex.org/W2033477411","https://openalex.org/W2034234432","https://openalex.org/W2041563548","https://openalex.org/W2041684917","https://openalex.org/W2047515818","https://openalex.org/W2049219350","https://openalex.org/W2054437396","https://openalex.org/W2067313886","https://openalex.org/W2069159962","https://openalex.org/W2069671092","https://openalex.org/W2075998338","https://openalex.org/W2077441566","https://openalex.org/W2080514141","https://openalex.org/W2083013597","https://openalex.org/W2085581918","https://openalex.org/W2086867325","https://openalex.org/W2087542711","https://openalex.org/W2106353864","https://openalex.org/W2115329284","https://openalex.org/W2119393586","https://openalex.org/W2123871098","https://openalex.org/W2137029533","https://openalex.org/W2141870784","https://openalex.org/W2157590940","https://openalex.org/W2360313265"],"related_works":["https://openalex.org/W2028160813","https://openalex.org/W2092639334","https://openalex.org/W1721021809","https://openalex.org/W2386970577","https://openalex.org/W2986665254","https://openalex.org/W2358212530","https://openalex.org/W2377375707","https://openalex.org/W1552250021","https://openalex.org/W2062832849","https://openalex.org/W2895996474"],"abstract_inverted_index":{"Interior-point":[0],"methods":[1,6],"feature":[2],"prominently":[3],"among":[4],"numerical":[5],"for":[7],"inequality-constrained":[8],"optimization":[9],"problems,":[10],"and":[11,52,69,92],"involve":[12],"the":[13,28,55,63,66,87,90,95,105],"need":[14],"to":[15,48,65,83],"solve":[16,31,54],"a":[17,38,71],"sequence":[18],"of":[19,89,114],"linear":[20],"systems":[21],"that":[22,94,117],"typically":[23],"become":[24],"increasingly":[25],"ill-conditioned":[26],"with":[27],"iterations.":[29],"To":[30],"these":[32],"systems,":[33],"whose":[34],"original":[35,96],"form":[36],"has":[37,99],"nonsymmetric":[39],"$3\\times":[40],"3$":[41],"block":[42,50],"structure,":[43],"it":[44],"is":[45],"common":[46],"practice":[47],"perform":[49],"elimination":[51],"either":[53],"resulting":[56],"reduced":[57,107],"saddle-point":[58],"system,":[59],"or":[60],"further":[61],"reduce":[62],"system":[64],"Schur":[67],"complement":[68],"apply":[70],"symmetric":[72],"positive":[73],"definite":[74],"solver.":[75],"In":[76],"this":[77],"paper":[78],"we":[79],"use":[80],"energy":[81],"estimates":[82],"obtain":[84],"bounds":[85,103],"on":[86],"eigenvalues":[88],"matrices,":[91],"conclude":[93],"unreduced":[97],"matrix":[98],"more":[100],"favorable":[101],"eigenvalue":[102],"than":[104],"alternative":[106],"versions.":[108],"Our":[109],"analysis":[110],"includes":[111],"regularized":[112],"variants":[113],"those":[115],"matrices":[116],"do":[118],"not":[119],"require":[120],"typical":[121],"regularity":[122],"assumptions.":[123]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}