{"id":"https://openalex.org/W2090583473","doi":"https://doi.org/10.1002/nla.1680020207","title":"Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion","display_name":"Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion","publication_year":1995,"publication_date":"1995-03-01","ids":{"openalex":"https://openalex.org/W2090583473","doi":"https://doi.org/10.1002/nla.1680020207","mag":"2090583473"},"language":"en","primary_location":{"id":"doi:10.1002/nla.1680020207","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.1680020207","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with 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/A5040996725","display_name":"L. Elsner","orcid":null},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Ludwig Elsner","raw_affiliation_strings":["Fakulta\u0308t fu\u0308r Mathematik, Universita\u0308t Bielefeld, Postfach 8640, D-33613 Bielefeld, Germany","Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Bielefeld, Postfach 8640, D-33613 Bielefeld, Germany"],"affiliations":[{"raw_affiliation_string":"Fakulta\u0308t fu\u0308r Mathematik, Universita\u0308t Bielefeld, Postfach 8640, D-33613 Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]},{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Bielefeld, Postfach 8640, D-33613 Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109223923","display_name":"Chunyang He","orcid":null},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Chunyang He","raw_affiliation_strings":["Fakulta\u0308t fu\u0308r Mathematik, Technische Universita\u0308t Chemnitz-Zwickau, D-09107 Chemnitz, Germany","Fakult\u00e4t f\u00fcr Mathematik, Technische Universit\u00e4t Chemnitz-Zwickau, D 09107, Chemnitz, Germany"],"affiliations":[{"raw_affiliation_string":"Fakulta\u0308t fu\u0308r Mathematik, Technische Universita\u0308t Chemnitz-Zwickau, D-09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]},{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik, Technische Universit\u00e4t Chemnitz-Zwickau, D 09107, Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016940729","display_name":"Volker Mehrmann","orcid":"https://orcid.org/0000-0001-5051-2870"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Volker Mehrmann","raw_affiliation_strings":["Fakulta\u0308t fu\u0308r Mathematik, Technische Universita\u0308t Chemnitz-Zwickau, D-09107 Chemnitz, Germany","Fakult\u00e4t f\u00fcr Mathematik, Technische Universit\u00e4t Chemnitz-Zwickau, D 09107, Chemnitz, Germany"],"affiliations":[{"raw_affiliation_string":"Fakulta\u0308t fu\u0308r Mathematik, Technische Universita\u0308t Chemnitz-Zwickau, D-09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]},{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik, Technische Universit\u00e4t Chemnitz-Zwickau, D 09107, Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040996725"],"corresponding_institution_ids":["https://openalex.org/I20121455"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.22034549,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2","issue":"2","first_page":"155","last_page":"171"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.998199999332428,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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":0.8498779535293579},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.7145076394081116},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.6603013873100281},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.639287531375885},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.609136164188385},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5572691559791565},{"id":"https://openalex.org/keywords/dual-norm","display_name":"Dual norm","score":0.48315876722335815},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33796554803848267},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32735639810562134},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24252033233642578},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.08703646063804626},{"id":"https://openalex.org/keywords/normed-vector-space","display_name":"Normed vector space","score":0.08029255270957947},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.050353556871414185}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8498779535293579},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.7145076394081116},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.6603013873100281},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.639287531375885},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.609136164188385},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5572691559791565},{"id":"https://openalex.org/C100022809","wikidata":"https://www.wikidata.org/wiki/Q5310221","display_name":"Dual norm","level":3,"score":0.48315876722335815},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33796554803848267},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32735639810562134},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24252033233642578},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.08703646063804626},{"id":"https://openalex.org/C171739935","wikidata":"https://www.wikidata.org/wiki/Q726210","display_name":"Normed vector space","level":2,"score":0.08029255270957947},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.050353556871414185},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/nla.1680020207","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.1680020207","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.331.7689","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.7689","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www3.math.tu-berlin.de/ePrints/papers/pdf/ElsHM95.pdf","raw_type":"text"},{"id":"pmh:oai:pub.uni-bielefeld.de:1640789","is_oa":false,"landing_page_url":"https://pub.uni-bielefeld.de/record/1640789","pdf_url":null,"source":{"id":"https://openalex.org/S4306401624","display_name":"Publikationen an der Universit\u00e4t Bielefeld (Universit\u00e4t Bielefeld)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Elsner L, He C, Mehrmann V. Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion. <em>Numerical Linear Algebra with Applications</em>. 1995;2(2):155-171.","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1560429934","https://openalex.org/W2002357820","https://openalex.org/W2020742244","https://openalex.org/W2026968413","https://openalex.org/W2038430052","https://openalex.org/W2054560172","https://openalex.org/W2059586807","https://openalex.org/W2074771309","https://openalex.org/W2078172548","https://openalex.org/W2568342123","https://openalex.org/W2798909945","https://openalex.org/W4247145112","https://openalex.org/W6828452281"],"related_works":["https://openalex.org/W2147619060","https://openalex.org/W2910693632","https://openalex.org/W2978021564","https://openalex.org/W2888367694","https://openalex.org/W2057555084","https://openalex.org/W4366768782","https://openalex.org/W2374649169","https://openalex.org/W2018239771","https://openalex.org/W2023111059","https://openalex.org/W2090583473"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"study":[2],"the":[3,7,9,12,15,21,35,59,63,66,69,73],"problem":[4,38,70],"of":[5,11,27,65,71],"minimizing":[6],"norm,":[8,23],"norm":[10,36,64],"inverse":[13],"and":[14],"condition":[16,74],"number":[17,75],"with":[18],"respect":[19],"to":[20,57],"spectral":[22],"when":[24],"a":[25,28,41,78],"submatrix":[26],"matrix":[29],"can":[30,52],"be":[31,55],"chosen":[32],"arbitrarily.":[33],"For":[34,68],"minimization":[37],"we":[39,76],"give":[40,77],"different":[42],"proof":[43],"than":[44],"that":[45,61],"given":[46],"by":[47],"Davis/Kahan/Weinberger.":[48],"This":[49],"new":[50],"approach":[51],"then":[53],"also":[54],"used":[56],"characterize":[58],"completions":[60],"minimize":[62],"inverse.":[67],"optimizing":[72],"partial":[79],"result.":[80]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}