{"id":"https://openalex.org/W2580686072","doi":"https://doi.org/10.1080/00207160.2017.1285020","title":"A class of multilevel structured low-rank approximation arising in material processing","display_name":"A class of multilevel structured low-rank approximation arising in material processing","publication_year":2017,"publication_date":"2017-01-24","ids":{"openalex":"https://openalex.org/W2580686072","doi":"https://doi.org/10.1080/00207160.2017.1285020","mag":"2580686072"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2017.1285020","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1285020","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/A5058463880","display_name":"Jianchao Bai","orcid":"https://orcid.org/0000-0002-2394-8852"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jianchao Bai","raw_affiliation_strings":["School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100653942","display_name":"Jicheng Li","orcid":"https://orcid.org/0009-0008-3847-8778"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jicheng Li","raw_affiliation_strings":["School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006606703","display_name":"Junkai Deng","orcid":"https://orcid.org/0000-0001-6288-4241"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junkai Deng","raw_affiliation_strings":["State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058463880","https://openalex.org/A5100653942"],"corresponding_institution_ids":["https://openalex.org/I87445476"],"apc_list":null,"apc_paid":null,"fwci":0.7501,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.65499133,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"95","issue":"2","first_page":"329","last_page":"340"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9983000159263611,"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":0.9983000159263611,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9889000058174133,"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/mathematics","display_name":"Mathematics","score":0.7410919666290283},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5193356275558472},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5110281705856323},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.49884843826293945},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.49524322152137756},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49021798372268677},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.47880205512046814},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46616750955581665},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4529187083244324},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.43777209520339966},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.42968130111694336},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34034860134124756},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2068139612674713},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.09605741500854492}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7410919666290283},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5193356275558472},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5110281705856323},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.49884843826293945},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.49524322152137756},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49021798372268677},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.47880205512046814},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46616750955581665},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4529187083244324},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.43777209520339966},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.42968130111694336},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34034860134124756},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2068139612674713},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.09605741500854492},{"id":"https://openalex.org/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2017.1285020","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1285020","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":[{"id":"https://metadata.un.org/sdg/8","score":0.49000000953674316,"display_name":"Decent work and economic growth"}],"awards":[{"id":"https://openalex.org/G1102527662","display_name":null,"funder_award_id":"2014JM1029","funder_id":"https://openalex.org/F4320324173","funder_display_name":"Natural Science Foundation of Shaanxi Province"},{"id":"https://openalex.org/G2942941121","display_name":null,"funder_award_id":"11671318; 11171270; 51471126","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4704768954","display_name":null,"funder_award_id":"xkjc2014008","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G7105821205","display_name":null,"funder_award_id":"2014M552435","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320324173","display_name":"Natural Science Foundation of Shaanxi Province","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W191724716","https://openalex.org/W586904642","https://openalex.org/W653924242","https://openalex.org/W1602049633","https://openalex.org/W1970156439","https://openalex.org/W1994320209","https://openalex.org/W2014092582","https://openalex.org/W2045079045","https://openalex.org/W2048558317","https://openalex.org/W2050958540","https://openalex.org/W2070642658","https://openalex.org/W2076566842","https://openalex.org/W2077482036","https://openalex.org/W2078701381","https://openalex.org/W2087196505","https://openalex.org/W2087648855","https://openalex.org/W2089472575","https://openalex.org/W2092423825","https://openalex.org/W2110096996","https://openalex.org/W2138505091","https://openalex.org/W2471988522","https://openalex.org/W2500090022","https://openalex.org/W2617156021","https://openalex.org/W2778808770","https://openalex.org/W2989457786","https://openalex.org/W4245345046"],"related_works":["https://openalex.org/W2560215812","https://openalex.org/W2949601986","https://openalex.org/W3106318770","https://openalex.org/W3144354057","https://openalex.org/W4385556248","https://openalex.org/W1986680416","https://openalex.org/W3213035342","https://openalex.org/W78474372","https://openalex.org/W4386753494","https://openalex.org/W3213049004"],"abstract_inverted_index":{"This":[0],"work":[1],"is":[2],"devoted":[3],"to":[4,43,96,103],"studying":[5],"the":[6,14,24,33,38,52,59,63,81,84,87,92,113,117],"problem":[7,35],"of":[8,16,32,62,83,86,112,116],"approximating":[9],"a":[10,56],"given":[11],"matrix":[12,20],"by":[13,50],"product":[15],"two":[17,47,74],"low-rank":[18],"structured":[19],"which":[21,67],"arises":[22],"in":[23,110],"material":[25],"processing.":[26],"Firstly,":[27],"we":[28,79],"analyse":[29],"some":[30],"properties":[31],"original":[34],"and":[36,55,90],"utilize":[37],"alternating":[39],"least":[40],"squares":[41],"method":[42,107],"reformulate":[44],"it":[45],"into":[46,73],"subproblems.":[48],"Then":[49],"using":[51],"Gramian":[53],"representation":[54],"Vandermonde-like":[57],"transformation,":[58],"feasible":[60],"sets":[61],"subproblems":[64],"are":[65,101],"characterized,":[66],"makes":[68],"them":[69],"be":[70],"respectively":[71],"transformed":[72],"unconstrained":[75],"minimization":[76],"problems.":[77],"Finally,":[78],"derive":[80],"expressions":[82],"gradients":[85],"objective":[88,118],"functions":[89],"apply":[91],"gradient":[93],"descent":[94],"algorithm":[95],"solve":[97],"them.":[98],"Numerical":[99],"examples":[100],"tested":[102],"show":[104],"that":[105],"our":[106],"performs":[108],"well":[109],"terms":[111],"residual":[114],"error":[115],"function.":[119]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-22T08:38:42.863108","created_date":"2025-10-10T00:00:00"}
