{"id":"https://openalex.org/W7160940399","doi":"https://doi.org/10.48550/arxiv.2605.08091","title":"Unitary-Invariant Decomposition of Reducible Total Least Squares Core Problems","display_name":"Unitary-Invariant Decomposition of Reducible Total Least Squares Core Problems","publication_year":2026,"publication_date":"2026-04-02","ids":{"openalex":"https://openalex.org/W7160940399","doi":"https://doi.org/10.48550/arxiv.2605.08091"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.08091","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.08091","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.08091","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109855507","display_name":"Sijia Yu","orcid":"https://orcid.org/0000-0001-5963-0427"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu, Sijia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135959907","display_name":"Bruno Carpentieri","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carpentieri, Bruno","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056265105","display_name":"Yan\u2010Fei Jing","orcid":"https://orcid.org/0000-0002-6120-9583"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jing, Yan-Fei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.8514000177383423,"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":0.8514000177383423,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.08479999750852585,"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":0.019200000911951065,"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/linear-subspace","display_name":"Linear subspace","score":0.5612999796867371},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.5249999761581421},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.4943999946117401},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4523000121116638},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.4410000145435333},{"id":"https://openalex.org/keywords/core","display_name":"Core (optical fiber)","score":0.429500013589859},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.4260999858379364},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.42149999737739563}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7156999707221985},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.5612999796867371},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.5249999761581421},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.4943999946117401},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4523000121116638},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4410000145435333},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.429500013589859},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.4260999858379364},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.42149999737739563},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.3944000005722046},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.388700008392334},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.35190001130104065},{"id":"https://openalex.org/C54654531","wikidata":"https://www.wikidata.org/wiki/Q6073574","display_name":"Irreducible component","level":5,"score":0.3504999876022339},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.3434000015258789},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.34220001101493835},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.31529998779296875},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3125999867916107},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31189998984336853},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.31040000915527344},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.30649998784065247},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3043000102043152},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3025999963283539},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2865999937057495},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.259799987077713},{"id":"https://openalex.org/C96214315","wikidata":"https://www.wikidata.org/wiki/Q727103","display_name":"Unitary matrix","level":3,"score":0.2533999979496002},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.25209999084472656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.08091","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.08091","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.08091","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.08091","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"analysis":[1],"of":[2,14,84,103],"a":[3,30,73,126],"total":[4],"least":[5],"square":[6],"problem":[7,32],"(TLS)":[8],"can":[9],"be":[10],"reduced":[11],"to":[12,121,138],"that":[13,130],"an":[15,146],"associated":[16,106],"core":[17,31,86],"problem,":[18],"which":[19,118],"typically":[20],"has":[21],"lower":[22],"dimension":[23],"and":[24,46,53,75,98,141],"improved":[25],"solubility":[26],"properties.":[27,49],"Nevertheless,":[28],"even":[29],"may":[33],"remain":[34],"reducible,":[35],"admitting":[36],"further":[37],"decomposition":[38,83],"into":[39,88],"irreducible":[40,90,122,131],"component":[41,62,91,123,132],"subproblems":[42,133],"with":[43,107],"simpler":[44],"structure":[45,102],"better":[47],"analytical":[48],"However,":[50],"no":[51],"systematic":[52],"invariant":[54],"procedure":[55],"is":[56,78],"available":[57],"for":[58,80],"identifying":[59],"all":[60,114],"such":[61],"subproblems,":[63,109],"either":[64,66],"over":[65,94],"real":[67],"or":[68],"complex":[69,96,115],"field.In":[70],"this":[71],"paper,":[72],"complete":[74],"constructive":[76],"framework":[77],"developed":[79],"the":[81,95,100,110],"exact":[82],"TLS":[85],"problems":[87],"unitary-unique":[89],"subproblems.By":[92],"working":[93],"field":[97],"exploiting":[99],"spectral":[101],"covariance":[104],"operators":[105],"C-subset":[108],"proposed":[111],"strategy":[112],"yields":[113],"indivisible":[116],"subspaces":[117],"will":[119],"lead":[120],"sub-problems.":[124],"As":[125],"consequence,":[127],"we":[128],"prove":[129],"are":[134],"uniquely":[135],"determined":[136],"up":[137],"unitary":[139],"transformations":[140],"permutation,":[142],"thereby":[143],"partially":[144],"resolving":[145],"open":[147],"question":[148],"left":[149],"in":[150],"Yu,":[151],"Jing.":[152],"SIAM":[153],"J.":[154],"Matrix":[155],"Anal.":[156],"Appl.,":[157],"46":[158],"(2025).":[159]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-13T00:00:00"}