{"id":"https://openalex.org/W1941583664","doi":"https://doi.org/10.1090/s0025-5718-06-01913-2","title":"On mixed and componentwise condition numbers for Moore\u2013Penrose inverse and linear least squares problems","display_name":"On mixed and componentwise condition numbers for Moore\u2013Penrose inverse and linear least squares problems","publication_year":2006,"publication_date":"2006-11-02","ids":{"openalex":"https://openalex.org/W1941583664","doi":"https://doi.org/10.1090/s0025-5718-06-01913-2","mag":"1941583664"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-06-01913-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01913-2","pdf_url":"https://www.ams.org/mcom/2007-76-258/S0025-5718-06-01913-2/S0025-5718-06-01913-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2007-76-258/S0025-5718-06-01913-2/S0025-5718-06-01913-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079608792","display_name":"Felipe Cucker","orcid":"https://orcid.org/0000-0002-4569-3248"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Felipe Cucker","raw_affiliation_strings":["Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong, P.R. of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong, P.R. of China","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009395387","display_name":"Huaian Diao","orcid":"https://orcid.org/0000-0002-3787-9608"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Huaian Diao","raw_affiliation_strings":["Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong, P.R. of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong, P.R. of China","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014988509","display_name":"Yimin Wei","orcid":"https://orcid.org/0000-0001-6192-0546"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yimin Wei","raw_affiliation_strings":["School of Mathematical Sciences, Fudan University, Shanghai 200433 and Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education, P.R. of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Fudan University, Shanghai 200433 and Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education, P.R. of China","institution_ids":["https://openalex.org/I24943067"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.9928,"has_fulltext":true,"cited_by_count":89,"citation_normalized_percentile":{"value":0.93449487,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"76","issue":"258","first_page":"947","last_page":"963"},"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":0.9979000091552734,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9940000176429749,"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/mathematics","display_name":"Mathematics","score":0.9120795726776123},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6530996561050415},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6429013609886169},{"id":"https://openalex.org/keywords/moore\u2013penrose-pseudoinverse","display_name":"Moore\u2013Penrose pseudoinverse","score":0.6124482154846191},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5698187351226807},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4961021840572357},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.47296613454818726},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.4686773419380188},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44338247179985046},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23932519555091858},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1732667088508606},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08752438426017761}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9120795726776123},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6530996561050415},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6429013609886169},{"id":"https://openalex.org/C21556879","wikidata":"https://www.wikidata.org/wiki/Q43219517","display_name":"Moore\u2013Penrose pseudoinverse","level":3,"score":0.6124482154846191},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5698187351226807},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4961021840572357},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.47296613454818726},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.4686773419380188},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44338247179985046},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23932519555091858},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1732667088508606},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08752438426017761},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-06-01913-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01913-2","pdf_url":"https://www.ams.org/mcom/2007-76-258/S0025-5718-06-01913-2/S0025-5718-06-01913-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.109.4233","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.109.4233","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2007-76-258/S0025-5718-06-01913-2/S0025-5718-06-01913-2.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-06-01913-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01913-2","pdf_url":"https://www.ams.org/mcom/2007-76-258/S0025-5718-06-01913-2/S0025-5718-06-01913-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1941583664.pdf","grobid_xml":"https://content.openalex.org/works/W1941583664.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W63662626","https://openalex.org/W83404773","https://openalex.org/W104974959","https://openalex.org/W658559791","https://openalex.org/W1514966789","https://openalex.org/W1530239534","https://openalex.org/W1970566262","https://openalex.org/W2015517273","https://openalex.org/W2023782398","https://openalex.org/W2027634563","https://openalex.org/W2030638350","https://openalex.org/W2060854423","https://openalex.org/W2066008381","https://openalex.org/W2078488968","https://openalex.org/W2090329912","https://openalex.org/W2140431525","https://openalex.org/W2150200785","https://openalex.org/W6600662151","https://openalex.org/W6632463696","https://openalex.org/W6732553836"],"related_works":["https://openalex.org/W2377937346","https://openalex.org/W1797940506","https://openalex.org/W2077909046","https://openalex.org/W1577277867","https://openalex.org/W2032268867","https://openalex.org/W4385273312","https://openalex.org/W2350269050","https://openalex.org/W4225689497","https://openalex.org/W1978915693","https://openalex.org/W2493516920"],"abstract_inverted_index":{"Classical":[0],"condition":[1,37,68],"numbers":[2,38,69],"are":[3,44],"normwise:":[4],"they":[5],"measure":[6],"the":[7,23,61,64,71,74,81,95],"size":[8],"of":[9,25,46,73,83,87],"both":[10,93],"input":[11],"perturbations":[12],"and":[13,50,66,85],"output":[14],"errors":[15],"using":[16],"some":[17],"norms.":[18],"To":[19],"take":[20],"into":[21],"account":[22],"relative":[24],"each":[26],"data":[27,34,96],"component,":[28],"and,":[29],"in":[30],"particular,":[31],"a":[32],"possible":[33],"sparseness,":[35],"componentwise":[36,67],"have":[39,98],"been":[40],"increasingly":[41],"considered.":[42],"These":[43],"mostly":[45],"two":[47],"kinds:":[48],"mixed":[49,65],"componentwise.":[51],"In":[52,92],"this":[53],"paper,":[54],"we":[55],"give":[56],"explicit":[57],"expressions,":[58],"computable":[59],"from":[60],"data,":[62],"for":[63,70,80],"computation":[72,82],"Moore\u00e2\u0080\u0093Penrose":[75],"inverse":[76],"as":[77,79],"well":[78],"solutions":[84],"residues":[86],"linear":[88],"least":[89],"squares":[90],"problems.":[91],"cases":[94],"matrices":[97],"full":[99],"column":[100],"(row)":[101],"rank.":[102]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}