{"id":"https://openalex.org/W2966608018","doi":"https://doi.org/10.1007/s11075-019-00785-9","title":"Condition numbers of the multidimensional total least squares problems having more than one solution","display_name":"Condition numbers of the multidimensional total least squares problems having more than one solution","publication_year":2019,"publication_date":"2019-08-06","ids":{"openalex":"https://openalex.org/W2966608018","doi":"https://doi.org/10.1007/s11075-019-00785-9","mag":"2966608018"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-019-00785-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-019-00785-9","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5101497768","display_name":"Lingsheng Meng","orcid":"https://orcid.org/0000-0001-8996-0128"},"institutions":[{"id":"https://openalex.org/I4210152533","display_name":"Lanzhou University of Finance and Economics","ror":"https://ror.org/04v7yv031","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210152533"]},{"id":"https://openalex.org/I68986083","display_name":"Northwest Normal University","ror":"https://ror.org/00gx3j908","country_code":"CN","type":"education","lineage":["https://openalex.org/I68986083"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lingsheng Meng","raw_affiliation_strings":["College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, China","School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730070, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, China","institution_ids":["https://openalex.org/I68986083"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730070, China","institution_ids":["https://openalex.org/I4210152533"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062302772","display_name":"Bing Zheng","orcid":"https://orcid.org/0000-0003-0552-835X"},"institutions":[{"id":"https://openalex.org/I4210152533","display_name":"Lanzhou University of Finance and Economics","ror":"https://ror.org/04v7yv031","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210152533"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bing Zheng","raw_affiliation_strings":["School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730070, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730070, China","institution_ids":["https://openalex.org/I4210152533"]}]},{"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 and Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai, 200433, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai, 200433, China","institution_ids":["https://openalex.org/I24943067"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062302772"],"corresponding_institution_ids":["https://openalex.org/I4210152533"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.5975,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.89805356,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"84","issue":"3","first_page":"887","last_page":"908"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9998999834060669,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9998999834060669,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.953499972820282,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T14365","display_name":"Leaf Properties and Growth Measurement","score":0.9480999708175659,"subfield":{"id":"https://openalex.org/subfields/1110","display_name":"Plant Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8734421133995056},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.795676589012146},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6166157126426697},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5914027094841003},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5360264182090759},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.4853147864341736},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4662213623523712},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4475984573364258},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4174099564552307},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.4120776951313019},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22109588980674744},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1393509805202484},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13251709938049316},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.08693620562553406}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8734421133995056},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.795676589012146},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6166157126426697},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5914027094841003},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5360264182090759},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4853147864341736},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4662213623523712},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4475984573364258},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4174099564552307},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.4120776951313019},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22109588980674744},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1393509805202484},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13251709938049316},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.08693620562553406},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s11075-019-00785-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-019-00785-9","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/405785","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/405785","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/436117","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/436117","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"\u671f\u520a\u8bba\u6587"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/405649","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/405649","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/430082","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/430082","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"\u671f\u520a\u8bba\u6587"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2107453491","display_name":null,"funder_award_id":"11771099","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4324301372","display_name":null,"funder_award_id":"11701458","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5947849822","display_name":"\u6b63\u5219\u5316\u603b\u4f53\u6700\u5c0f\u4e8c\u4e58\u95ee\u9898\u7684\u9ad8\u6027\u80fd\u7b97\u6cd5\u53ca\u7406\u8bba\u7814\u7a76","funder_award_id":"11571004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W658559791","https://openalex.org/W1969219355","https://openalex.org/W1995376194","https://openalex.org/W2030255580","https://openalex.org/W2037727941","https://openalex.org/W2047978039","https://openalex.org/W2052261993","https://openalex.org/W2074702686","https://openalex.org/W2078488968","https://openalex.org/W2088028136","https://openalex.org/W2091559329","https://openalex.org/W2095692981","https://openalex.org/W2098709175","https://openalex.org/W2128900999","https://openalex.org/W2136651047","https://openalex.org/W2385681122","https://openalex.org/W2750836333","https://openalex.org/W2798909945","https://openalex.org/W3042168128","https://openalex.org/W3143949042","https://openalex.org/W4206428854","https://openalex.org/W4312258136"],"related_works":["https://openalex.org/W2978021564","https://openalex.org/W2888367694","https://openalex.org/W2057555084","https://openalex.org/W2039023896","https://openalex.org/W2154812892","https://openalex.org/W2018239771","https://openalex.org/W2028790718","https://openalex.org/W1762420609","https://openalex.org/W2134887131","https://openalex.org/W2592387312"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}