{"id":"https://openalex.org/W317962825","doi":"https://doi.org/10.1007/978-3-642-53703-5_55","title":"Solutions of Ill-Posed Linear Equations","display_name":"Solutions of Ill-Posed Linear Equations","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W317962825","doi":"https://doi.org/10.1007/978-3-642-53703-5_55","mag":"317962825"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-53703-5_55","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-53703-5_55","pdf_url":null,"source":{"id":"https://openalex.org/S2764900261","display_name":"Communications in computer and information science","issn_l":"1865-0929","issn":["1865-0929","1865-0937"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Computer and Information Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5001056457","display_name":"Yamian Peng","orcid":null},"institutions":[{"id":"https://openalex.org/I137506752","display_name":"North China University of Science and Technology","ror":"https://ror.org/04z4wmb81","country_code":"CN","type":"education","lineage":["https://openalex.org/I137506752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yamian Peng","raw_affiliation_strings":["College of Science, Hebei United University, Tangshan, 063009, Hebei, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Hebei United University, Tangshan, 063009, Hebei, P.R. China","institution_ids":["https://openalex.org/I137506752"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073389192","display_name":"Jincai Chang","orcid":"https://orcid.org/0000-0002-5605-2032"},"institutions":[{"id":"https://openalex.org/I137506752","display_name":"North China University of Science and Technology","ror":"https://ror.org/04z4wmb81","country_code":"CN","type":"education","lineage":["https://openalex.org/I137506752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jincai Chang","raw_affiliation_strings":["College of Science, Hebei United University, Tangshan, 063009, Hebei, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Hebei United University, Tangshan, 063009, Hebei, P.R. China","institution_ids":["https://openalex.org/I137506752"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100395059","display_name":"Yan Yan","orcid":"https://orcid.org/0000-0002-3674-7160"},"institutions":[{"id":"https://openalex.org/I137506752","display_name":"North China University of Science and Technology","ror":"https://ror.org/04z4wmb81","country_code":"CN","type":"education","lineage":["https://openalex.org/I137506752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan Yan","raw_affiliation_strings":["College of Science, Hebei United University, Tangshan, 063009, Hebei, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Hebei United University, Tangshan, 063009, Hebei, P.R. China","institution_ids":["https://openalex.org/I137506752"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I137506752"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18211921,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"536","last_page":"545"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12508","display_name":"Functional Equations Stability Results","score":0.9546999931335449,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12508","display_name":"Functional Equations Stability Results","score":0.9546999931335449,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.9093999862670898,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9031000137329102,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/grasp","display_name":"GRASP","score":0.7610594630241394},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5911339521408081},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5626459121704102},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.5348734855651855},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.48941221833229065},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4760065972805023},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44938531517982483},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4449920058250427},{"id":"https://openalex.org/keywords/well-posed-problem","display_name":"Well-posed problem","score":0.43960779905319214},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4168643355369568},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41515052318573},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41429266333580017},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1863812506198883},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06346216797828674},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06068575382232666},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.06015884876251221}],"concepts":[{"id":"https://openalex.org/C171268870","wikidata":"https://www.wikidata.org/wiki/Q1486676","display_name":"GRASP","level":2,"score":0.7610594630241394},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5911339521408081},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5626459121704102},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.5348734855651855},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.48941221833229065},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4760065972805023},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44938531517982483},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4449920058250427},{"id":"https://openalex.org/C106214006","wikidata":"https://www.wikidata.org/wiki/Q1455898","display_name":"Well-posed problem","level":2,"score":0.43960779905319214},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4168643355369568},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41515052318573},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41429266333580017},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1863812506198883},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06346216797828674},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06068575382232666},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.06015884876251221},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-53703-5_55","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-53703-5_55","pdf_url":null,"source":{"id":"https://openalex.org/S2764900261","display_name":"Communications in computer and information science","issn_l":"1865-0929","issn":["1865-0929","1865-0937"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Computer and Information Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W132318879","https://openalex.org/W299240732","https://openalex.org/W2047008106","https://openalex.org/W2898916015","https://openalex.org/W3141390961"],"related_works":["https://openalex.org/W195825275","https://openalex.org/W153415882","https://openalex.org/W2365527693","https://openalex.org/W3023921507","https://openalex.org/W2739650862","https://openalex.org/W2500993308","https://openalex.org/W4252024106","https://openalex.org/W2389121573","https://openalex.org/W3023000303","https://openalex.org/W4308301247"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}