{"id":"https://openalex.org/W2010435296","doi":"https://doi.org/10.1080/00207160008804956","title":"Perturbation analysis of singular linear systems with index one<sup>\u2217</sup>","display_name":"Perturbation analysis of singular linear systems with index one<sup>\u2217</sup>","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2010435296","doi":"https://doi.org/10.1080/00207160008804956","mag":"2010435296"},"language":"en","primary_location":{"id":"doi:10.1080/00207160008804956","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160008804956","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/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":true,"raw_author_name":"Yimin Wei","raw_affiliation_strings":["Department of Mathematics and Laboratory of Mathematics for Nonlinear Sciences , Fudan University , Shanghai, 200433, People's Republic of China ; Department of Mathematics and Laboratory of Mathematics for Nonlinear Sciences , Fudan University , Shanghai, 200433, People's Republic of China","Department of Mathematics and Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai 200433, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Laboratory of Mathematics for Nonlinear Sciences , Fudan University , Shanghai, 200433, People's Republic of China ; Department of Mathematics and Laboratory of Mathematics for Nonlinear Sciences , Fudan University , Shanghai, 200433, People's Republic of China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Department of Mathematics and Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai 200433, People's Republic of China","institution_ids":["https://openalex.org/I24943067"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014988509"],"corresponding_institution_ids":["https://openalex.org/I24943067"],"apc_list":null,"apc_paid":null,"fwci":1.3626,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.80712951,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"74","issue":"4","first_page":"483","last_page":"491"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9962000250816345,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9944000244140625,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7844635844230652},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.7358394861221313},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.5615834593772888},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.5592275261878967},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.5567829608917236},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5336537957191467},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4735395312309265},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33957821130752563},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.2587190270423889},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12203139066696167},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11817073822021484},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0965442955493927}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7844635844230652},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.7358394861221313},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.5615834593772888},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.5592275261878967},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.5567829608917236},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5336537957191467},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4735395312309265},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33957821130752563},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2587190270423889},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12203139066696167},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11817073822021484},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0965442955493927}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160008804956","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160008804956","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W83404773","https://openalex.org/W658559791","https://openalex.org/W1500921805","https://openalex.org/W1968647352","https://openalex.org/W1983992752","https://openalex.org/W1988741710","https://openalex.org/W1994892352","https://openalex.org/W1998209214","https://openalex.org/W2003137566","https://openalex.org/W2008093443","https://openalex.org/W2010114893","https://openalex.org/W2019006846","https://openalex.org/W2042151247","https://openalex.org/W2044111373","https://openalex.org/W2054182987","https://openalex.org/W2075665712","https://openalex.org/W2080919409","https://openalex.org/W2085207070","https://openalex.org/W2088060298","https://openalex.org/W2090847218","https://openalex.org/W2150287034","https://openalex.org/W2150997465","https://openalex.org/W2333836441","https://openalex.org/W4295016751"],"related_works":["https://openalex.org/W4327639758","https://openalex.org/W1998082046","https://openalex.org/W2116787190","https://openalex.org/W2154304710","https://openalex.org/W1532878563","https://openalex.org/W2019676381","https://openalex.org/W2387468633","https://openalex.org/W2037738710","https://openalex.org/W2006371715","https://openalex.org/W4225411471"],"abstract_inverted_index":{"A":[0],"new":[1],"perturbation":[2,28,42],"result":[3,43],"for":[4],"singular":[5],"but":[6],"consistent":[7],"linear":[8,33,46],"systems":[9],"with":[10],"coefficient":[11],"matrix":[12],"of":[13,30],"index":[14],"one":[15],"is":[16,22],"presented.":[17],"However,":[18],"if":[19],"the":[20,31],"system":[21],"inconsistent,":[23],"we":[24],"also":[25],"derive":[26],"a":[27,40],"bound":[29],"generalized":[32],"least":[34],"squares":[35],"solution.":[36],"Our":[37],"treatment":[38],"extends":[39],"classical":[41],"in":[44],"numerical":[45],"algebra.":[47]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}