{"id":"https://openalex.org/W1984633545","doi":"https://doi.org/10.1137/s0895479894271093","title":"Stability of Augmented System Factorizations in Interior-Point Methods","display_name":"Stability of Augmented System Factorizations in Interior-Point Methods","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W1984633545","doi":"https://doi.org/10.1137/s0895479894271093","mag":"1984633545"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479894271093","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479894271093","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5046109083","display_name":"Stephen J. Wright","orcid":"https://orcid.org/0000-0001-6815-7379"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Stephen Wright","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5046109083"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1689,"has_fulltext":false,"cited_by_count":98,"citation_normalized_percentile":{"value":0.94498239,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"18","issue":"1","first_page":"191","last_page":"222"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991000294685364,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9929999709129333,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7448561191558838},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.7344884872436523},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.6547067165374756},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6261618733406067},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.6233336329460144},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5829569101333618},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5443070530891418},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5326921939849854},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5066817402839661},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5006470680236816},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4962382912635803},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.4641292095184326},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.42487776279449463},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3498871326446533},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25576967000961304},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16993364691734314},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13705283403396606},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.07180997729301453}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7448561191558838},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.7344884872436523},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.6547067165374756},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6261618733406067},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.6233336329460144},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5829569101333618},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5443070530891418},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5326921939849854},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5066817402839661},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5006470680236816},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4962382912635803},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.4641292095184326},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.42487776279449463},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3498871326446533},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25576967000961304},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16993364691734314},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13705283403396606},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07180997729301453},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0895479894271093","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479894271093","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.36.3142","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.3142","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mcs.anl.gov/~wright/papers/P446.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.55.9080","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.55.9080","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://info.mcs.anl.gov/pub/tech_reports/reports/P446.ps.Z","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1983709472","https://openalex.org/W2013986021","https://openalex.org/W2014885585","https://openalex.org/W2019744552","https://openalex.org/W2030490984","https://openalex.org/W2031392034","https://openalex.org/W2036622774","https://openalex.org/W2036675242","https://openalex.org/W2043868859","https://openalex.org/W2044061073","https://openalex.org/W2046222402","https://openalex.org/W2050897335","https://openalex.org/W2063176644","https://openalex.org/W2084743588","https://openalex.org/W2086867325","https://openalex.org/W2093903024","https://openalex.org/W2146325267","https://openalex.org/W2571013927"],"related_works":["https://openalex.org/W4378529241","https://openalex.org/W2483828597","https://openalex.org/W2794559785","https://openalex.org/W2070124887","https://openalex.org/W2088213153","https://openalex.org/W2950631682","https://openalex.org/W2026488547","https://openalex.org/W3108517195","https://openalex.org/W4225411471","https://openalex.org/W2372971227"],"abstract_inverted_index":{"Some":[0],"implementations":[1],"of":[2,14,19,34],"interior-point":[3,59],"algorithms":[4],"obtain":[5],"their":[6],"search":[7],"directions":[8],"by":[9,48],"solving":[10],"symmetric":[11],"indefinite":[12],"systems":[13,27],"linear":[15,69,99],"equations.":[16],"The":[17],"conditioning":[18],"the":[20,35,45,58,67,88,98],"coefficient":[21],"matrices":[22],"in":[23],"these":[24],"so-called":[25],"augmented":[26],"deteriorates":[28],"on":[29],"later":[30],"iterations,":[31],"as":[32],"some":[33],"diagonal":[36],"elements":[37],"grow":[38],"without":[39],"bound.":[40],"Despite":[41],"this":[42],"apparent":[43],"difficulty,":[44],"steps":[46],"produced":[47],"standard":[49],"factorization":[50],"procedures":[51],"are":[52],"often":[53],"accurate":[54],"enough":[55],"to":[56,61,63,77,105],"allow":[57],"method":[60],"converge":[62],"high":[64,79,111],"accuracy.":[65],"When":[66],"underlying":[68],"program":[70,100],"is":[71,101,113],"nondegenerate,":[72],"we":[73],"show":[74],"that":[75,85],"convergence":[76,104],"arbitrarily":[78,110],"accuracy":[80,107],"occurs,":[81],"at":[82],"a":[83],"rate":[84],"closely":[86],"approximates":[87],"theory.":[89],"We":[90],"also":[91],"explain":[92],"and":[93],"demonstrate":[94],"what":[95],"happens":[96],"when":[97],"degenerate,":[102],"where":[103],"acceptable":[106],"(but":[108],"not":[109],"accuracy)":[112],"usually":[114],"obtained.":[115]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}