{"id":"https://openalex.org/W2802886200","doi":"https://doi.org/10.1137/16m108152x","title":"Refining the Lower Bound on the Positive Eigenvalues of Saddle Point Matrices with Insights on the Interactions between the Blocks","display_name":"Refining the Lower Bound on the Positive Eigenvalues of Saddle Point Matrices with Insights on the Interactions between the Blocks","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2802886200","doi":"https://doi.org/10.1137/16m108152x","mag":"2802886200"},"language":"en","primary_location":{"id":"doi:10.1137/16m108152x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m108152x","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":true,"oa_status":"green","oa_url":"https://researchportal.unamur.be/en/publications/544246bb-eda8-4b13-b80a-ea2b75ca5836","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5106497787","display_name":"Daniel Ruiz","orcid":"https://orcid.org/0000-0002-3867-0179"},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I205747304","display_name":"Institut National Polytechnique de Toulouse","ror":"https://ror.org/033p9g875","country_code":"FR","type":"education","lineage":["https://openalex.org/I205747304"]},{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]},{"id":"https://openalex.org/I4210119061","display_name":"Institut de Recherche en Informatique de Toulouse","ror":"https://ror.org/01rx4qw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]},{"id":"https://openalex.org/I4210152422","display_name":"Universit\u00e9 Toulouse - Jean Jaur\u00e8s","ror":"https://ror.org/04ezk3x31","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210152422"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Daniel Ruiz","raw_affiliation_strings":["IRIT-APO - Algorithmes Parall\u00e8les et Optimisation (Institut de recherche en informatique de Toulouse - IRIT\r\n2 rue Charles Camichel \r\n31071 Toulouse Cedex 7 \r\n - France)","Toulouse INP - Institut National Polytechnique (Toulouse) (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRIT-APO - Algorithmes Parall\u00e8les et Optimisation (Institut de recherche en informatique de Toulouse - IRIT\r\n2 rue Charles Camichel \r\n31071 Toulouse Cedex 7 \r\n - France)","institution_ids":["https://openalex.org/I4210152422","https://openalex.org/I134560555","https://openalex.org/I4210119061","https://openalex.org/I3131550300","https://openalex.org/I4210160189"]},{"raw_affiliation_string":"Toulouse INP - Institut National Polytechnique (Toulouse) (France)","institution_ids":["https://openalex.org/I205747304"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106181985","display_name":"Annick Sartenaer","orcid":"https://orcid.org/0000-0003-4844-5239"},"institutions":[{"id":"https://openalex.org/I149768937","display_name":"University of Namur","ror":"https://ror.org/03d1maw17","country_code":"BE","type":"education","lineage":["https://openalex.org/I149768937"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Annick Sartenaer","raw_affiliation_strings":["NaXys - Namur Center for Complex Systems [Namur] (Rempart de la Vierge 8, 5000 Namur - Belgium)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NaXys - Namur Center for Complex Systems [Namur] (Rempart de la Vierge 8, 5000 Namur - Belgium)","institution_ids":["https://openalex.org/I149768937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005032225","display_name":"Charlotte Tannier","orcid":null},"institutions":[{"id":"https://openalex.org/I149768937","display_name":"University of Namur","ror":"https://ror.org/03d1maw17","country_code":"BE","type":"education","lineage":["https://openalex.org/I149768937"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Charlotte Tannier","raw_affiliation_strings":["NaXys - Namur Center for Complex Systems [Namur] (Rempart de la Vierge 8, 5000 Namur - Belgium)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NaXys - Namur Center for Complex Systems [Namur] (Rempart de la Vierge 8, 5000 Namur - Belgium)","institution_ids":["https://openalex.org/I149768937"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2145,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.54250131,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"39","issue":"2","first_page":"712","last_page":"736"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9976999759674072,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.8608607053756714},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.8137122988700867},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8025652170181274},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7757145166397095},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.610090970993042},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5191342234611511},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.5116422772407532},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.453849196434021},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4504193663597107},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44938531517982483},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4419705271720886},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.41925686597824097},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2984127104282379},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.266065388917923},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22238630056381226},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.08486023545265198},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08135098218917847}],"concepts":[{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.8608607053756714},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.8137122988700867},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8025652170181274},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7757145166397095},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.610090970993042},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5191342234611511},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.5116422772407532},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.453849196434021},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4504193663597107},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44938531517982483},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4419705271720886},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.41925686597824097},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2984127104282379},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.266065388917923},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22238630056381226},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.08486023545265198},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08135098218917847},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/16m108152x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m108152x","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:pure.unamur.be:openaire/544246bb-eda8-4b13-b80a-ea2b75ca5836","is_oa":true,"landing_page_url":"https://researchportal.unamur.be/en/publications/544246bb-eda8-4b13-b80a-ea2b75ca5836","pdf_url":null,"source":{"id":"https://openalex.org/S4406922457","display_name":"Repository of the University of Namur","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ruiz, D, Sartenaer, A & Tannier, C 2018, 'Refining the lower bound on the positive eigenvalues of saddle point matrices with insights on the interactions between the blocks', SIAM Journal on Matrix Analysis and Applications, vol. 39, no. 2, pp. 712-736. https://doi.org/10.1137/16M108152X","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:oatao.univ-toulouse.fr:22364","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401987","display_name":"Open Archive Toulouse Archive Ouverte (University of Toulouse)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I17866349","host_organization_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","host_organization_lineage":["https://openalex.org/I17866349"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:HAL:hal-02348261v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02348261","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications, 2018, 39 (2), pp.712-736. ⟨10.1137/16M108152X⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:pure.unamur.be:openaire/544246bb-eda8-4b13-b80a-ea2b75ca5836","is_oa":true,"landing_page_url":"https://researchportal.unamur.be/en/publications/544246bb-eda8-4b13-b80a-ea2b75ca5836","pdf_url":null,"source":{"id":"https://openalex.org/S4406922457","display_name":"Repository of the University of Namur","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ruiz, D, Sartenaer, A & Tannier, C 2018, 'Refining the lower bound on the positive eigenvalues of saddle point matrices with insights on the interactions between the blocks', SIAM Journal on Matrix Analysis and Applications, vol. 39, no. 2, pp. 712-736. https://doi.org/10.1137/16M108152X","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2840746402","display_name":null,"funder_award_id":"ANR-11-MONU-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3979525718","display_name":null,"funder_award_id":"ANR-11-MONU-004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321454","display_name":"Belgian Federal Science Policy Office","ror":"https://ror.org/01fapfv42"},{"id":"https://openalex.org/F4320338463","display_name":"CHIST-ERA","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1985852691","https://openalex.org/W1999331305","https://openalex.org/W2003550247","https://openalex.org/W2048360198","https://openalex.org/W2067313886","https://openalex.org/W2115291951","https://openalex.org/W2141870784"],"related_works":["https://openalex.org/W1574104658","https://openalex.org/W4236459141","https://openalex.org/W4205304778","https://openalex.org/W2020252434","https://openalex.org/W73248859","https://openalex.org/W2584253892","https://openalex.org/W2350324449","https://openalex.org/W119381072","https://openalex.org/W2034033896","https://openalex.org/W2094891943"],"abstract_inverted_index":{"Efficiently":[0],"solving":[1],"saddle":[2,138],"point":[3,139],"systems":[4,8,20],"like":[5,84],"Karush--Kuhn--Tucker":[6],"(KKT)":[7],"is":[9,52],"crucial":[10],"for":[11],"many":[12],"algorithms":[13],"in":[14,26,98,105,121],"constrained":[15],"nonlinear":[16],"continuous":[17],"optimization.":[18],"Such":[19],"can":[21],"be":[22,113],"very":[23,34,118],"ill":[24],"conditioned,":[25],"particular":[27],"when":[28],"the":[29,69,78,108,122,134,142],"(1,1)":[30,66,123],"block":[31,67,71],"has":[32],"few":[33,117],"small":[35,58,119],"eigenvalues":[36,120,136],"(see":[37],"Rusten":[38],"and":[39,68,104],"Winther":[40],"[SIAM":[41],"J.":[42],"Matrix":[43],"Anal.":[44],"Appl.,":[45],"13":[46],"(1992),":[47],"pp.":[48],"887--904]).":[49],"However,":[50],"it":[51],"commonly":[53],"observed":[54],"that":[55,74],"despite":[56],"these":[57,116],"eigenvalues,":[59],"some":[60,91,101],"sort":[61],"of":[62,80,93,110,137,141],"interaction":[63],"between":[64],"this":[65,87,94],"(1,2)":[70],"actually":[72],"occurs":[73],"may":[75],"influence":[76],"strongly":[77],"convergence":[79,109],"Krylov":[81],"subspace":[82],"methods":[83],"Minres.":[85],"In":[86],"paper,":[88],"we":[89],"highlight":[90],"aspects":[92],"interaction.":[95],"We":[96,125],"illustrate":[97],"particular,":[99],"with":[100],"examples,":[102],"how":[103],"which":[106],"circumstances":[107],"Minres":[111],"might":[112],"affected":[114],"by":[115],"block.":[124],"further":[126],"derive":[127],"theoretically":[128],"a":[129],"tighter":[130],"lower":[131],"bound":[132],"on":[133],"positive":[135],"matrices":[140],"KKT":[143],"form.":[144]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-20T22:02:38.213706","created_date":"2025-10-10T00:00:00"}