{"id":"https://openalex.org/W7162545424","doi":"https://doi.org/10.1137/25m1788312","title":"Efficient Estimate for the Optimal Backward Error of the Multidimensional Total Least Squares","display_name":"Efficient Estimate for the Optimal Backward Error of the Multidimensional Total Least Squares","publication_year":2026,"publication_date":"2026-05-27","ids":{"openalex":"https://openalex.org/W7162545424","doi":"https://doi.org/10.1137/25m1788312"},"language":"en","primary_location":{"id":"doi:10.1137/25m1788312","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1788312","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and 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/A5070712374","display_name":"Jiali Shan","orcid":null},"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":"Jiali Shan","raw_affiliation_strings":["School of Mathematical Sciences, Fudan University, Shanghai 200433, People\u2019s Republic of China"],"raw_orcid":"https://orcid.org/0009-0000-6514-9349","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Fudan University, Shanghai 200433, People\u2019s Republic of China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027708303","display_name":"Ye Wei","orcid":"https://orcid.org/0000-0001-9805-1241"},"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":["Corresponding author.\u00a0School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai 200433, People\u2019s Republic of China"],"raw_orcid":"https://orcid.org/0000-0001-6192-0546","affiliations":[{"raw_affiliation_string":"Corresponding author.\u00a0School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai 200433, People\u2019s Republic of China","institution_ids":["https://openalex.org/I24943067"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I24943067"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.69750195,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"47","issue":"2","first_page":"649","last_page":"672"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9632999897003174,"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":0.9632999897003174,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.0071000000461936,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.006399999838322401,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.5098000168800354},{"id":"https://openalex.org/keywords/total-least-squares","display_name":"Total least squares","score":0.4830000102519989},{"id":"https://openalex.org/keywords/non-linear-least-squares","display_name":"Non-linear least squares","score":0.3885999917984009},{"id":"https://openalex.org/keywords/generalized-least-squares","display_name":"Generalized least squares","score":0.34040001034736633},{"id":"https://openalex.org/keywords/linear-least-squares","display_name":"Linear least squares","score":0.3287000060081482},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.31869998574256897}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7684000134468079},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5098000168800354},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4943000078201294},{"id":"https://openalex.org/C169241690","wikidata":"https://www.wikidata.org/wiki/Q7828122","display_name":"Total least squares","level":3,"score":0.4830000102519989},{"id":"https://openalex.org/C45923927","wikidata":"https://www.wikidata.org/wiki/Q3319230","display_name":"Non-linear least squares","level":3,"score":0.3885999917984009},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38119998574256897},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3540000021457672},{"id":"https://openalex.org/C188649462","wikidata":"https://www.wikidata.org/wiki/Q2246261","display_name":"Generalized least squares","level":3,"score":0.34040001034736633},{"id":"https://openalex.org/C58663186","wikidata":"https://www.wikidata.org/wiki/Q6553462","display_name":"Linear least squares","level":3,"score":0.3287000060081482},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.31869998574256897},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.3125999867916107},{"id":"https://openalex.org/C126090379","wikidata":"https://www.wikidata.org/wiki/Q6094424","display_name":"Iteratively reweighted least squares","level":4,"score":0.29499998688697815},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.26919999718666077},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/25m1788312","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1788312","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G116967129","display_name":null,"funder_award_id":"123B1008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2915528550","display_name":null,"funder_award_id":"U24A2001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6666115934","display_name":null,"funder_award_id":"12271108","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7742448768","display_name":null,"funder_award_id":"23JC1400501","funder_id":"https://openalex.org/F4320321885","funder_display_name":"Science and Technology Commission of Shanghai Municipality"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321885","display_name":"Science and Technology Commission of Shanghai Municipality","ror":"https://ror.org/03kt66j61"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1963961606","https://openalex.org/W1977181654","https://openalex.org/W1977579021","https://openalex.org/W1982851849","https://openalex.org/W1995883331","https://openalex.org/W1997470526","https://openalex.org/W2007191224","https://openalex.org/W2008229822","https://openalex.org/W2014540466","https://openalex.org/W2018978449","https://openalex.org/W2020804487","https://openalex.org/W2035741281","https://openalex.org/W2040012448","https://openalex.org/W2053000670","https://openalex.org/W2074702686","https://openalex.org/W2078643711","https://openalex.org/W2088028136","https://openalex.org/W2093406485","https://openalex.org/W2094358944","https://openalex.org/W2115727068","https://openalex.org/W2117756735","https://openalex.org/W2118550318","https://openalex.org/W2127345882","https://openalex.org/W2150205499","https://openalex.org/W2163924219","https://openalex.org/W2494638940","https://openalex.org/W2750836333","https://openalex.org/W2798427052","https://openalex.org/W2809307912","https://openalex.org/W2964361301","https://openalex.org/W3044740813","https://openalex.org/W3108353645","https://openalex.org/W4206428854","https://openalex.org/W4210601051","https://openalex.org/W4213311204","https://openalex.org/W4229706427","https://openalex.org/W4251295351","https://openalex.org/W4312258136","https://openalex.org/W4318764269","https://openalex.org/W4385616608","https://openalex.org/W4399521853","https://openalex.org/W4403198644","https://openalex.org/W4411570656","https://openalex.org/W4414336147"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-05-28T06:19:16.900634","created_date":"2026-05-28T00:00:00"}