{"id":"https://openalex.org/W2963925668","doi":"https://doi.org/10.1137/18m1169321","title":"Numerical Algorithms on the Affine Grassmannian","display_name":"Numerical Algorithms on the Affine Grassmannian","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2963925668","doi":"https://doi.org/10.1137/18m1169321","mag":"2963925668"},"language":"en","primary_location":{"id":"doi:10.1137/18m1169321","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1169321","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/A5050794507","display_name":"Lek\u2010Heng Lim","orcid":"https://orcid.org/0000-0002-9808-0138"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lek-Heng Lim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064666012","display_name":"Ken Sze-Wai Wong","orcid":"https://orcid.org/0000-0002-5235-560X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ken Sze-Wai Wong","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5235-560X","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100775242","display_name":"Ke Ye","orcid":"https://orcid.org/0000-0002-3193-7264"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ke Ye","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050794507"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3998,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.83562858,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"40","issue":"2","first_page":"371","last_page":"393"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9912999868392944,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.991100013256073,"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/grassmannian","display_name":"Grassmannian","score":0.8727993369102478},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8556891083717346},{"id":"https://openalex.org/keywords/affine-hull","display_name":"Affine hull","score":0.7044937610626221},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.6522457599639893},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6371291279792786},{"id":"https://openalex.org/keywords/affine-space","display_name":"Affine space","score":0.6030171513557434},{"id":"https://openalex.org/keywords/affine-combination","display_name":"Affine combination","score":0.5965931415557861},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.44708991050720215},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4327552914619446},{"id":"https://openalex.org/keywords/affine-shape-adaptation","display_name":"Affine shape adaptation","score":0.43070778250694275},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4261767566204071},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3233673870563507}],"concepts":[{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.8727993369102478},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8556891083717346},{"id":"https://openalex.org/C112128483","wikidata":"https://www.wikidata.org/wiki/Q382504","display_name":"Affine hull","level":4,"score":0.7044937610626221},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.6522457599639893},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6371291279792786},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.6030171513557434},{"id":"https://openalex.org/C207221997","wikidata":"https://www.wikidata.org/wiki/Q938614","display_name":"Affine combination","level":3,"score":0.5965931415557861},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44708991050720215},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4327552914619446},{"id":"https://openalex.org/C18516315","wikidata":"https://www.wikidata.org/wiki/Q4688950","display_name":"Affine shape adaptation","level":4,"score":0.43070778250694275},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4261767566204071},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3233673870563507}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1169321","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1169321","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/G2771606194","display_name":null,"funder_award_id":"D15AP00109","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G4199670578","display_name":null,"funder_award_id":"FA9550-13-1-0133","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5686484291","display_name":null,"funder_award_id":"IIS 1546413","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6967058303","display_name":null,"funder_award_id":"11688101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8698799443","display_name":null,"funder_award_id":"11801548","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8817569772","display_name":null,"funder_award_id":"DMS-1057064","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1914597940","https://openalex.org/W1968637289","https://openalex.org/W1993962865","https://openalex.org/W2003361735","https://openalex.org/W2005400753","https://openalex.org/W2013257697","https://openalex.org/W2045512849","https://openalex.org/W2059134260","https://openalex.org/W2109409043","https://openalex.org/W2147631863","https://openalex.org/W2177347332","https://openalex.org/W2962777248","https://openalex.org/W2963346868","https://openalex.org/W3030910590","https://openalex.org/W3103861421"],"related_works":["https://openalex.org/W2077954576","https://openalex.org/W2101790592","https://openalex.org/W2964008969","https://openalex.org/W3022853753","https://openalex.org/W2106401644","https://openalex.org/W2180439206","https://openalex.org/W2306105624","https://openalex.org/W2783438186","https://openalex.org/W4300070731","https://openalex.org/W2963925668"],"abstract_inverted_index":{"The":[0],"affine":[1,11,28,34,58],"Grassmannian":[2,35],"is":[3,18],"a":[4,14,19,37],"noncompact":[5],"smooth":[6],"manifold":[7,39],"that":[8],"parameterizes":[9],"all":[10],"subspaces":[12],"of":[13,22],"fixed":[15],"dimension.":[16],"It":[17],"natural":[20],"generalization":[21],"Euclidean":[23],"space,":[24],"points":[25],"being":[26],"zero-dimensional":[27],"subspaces.":[29],"We":[30],"will":[31],"realize":[32],"the":[33,57,64],"as":[36],"matrix":[38],"and":[40,50,74],"extend":[41],"Riemannian":[42],"optimization":[43],"algorithms":[44],"including":[45],"steepest":[46],"descent,":[47],"Newton":[48],"method,":[49],"conjugate":[51],"gradient,":[52],"to":[53],"real-valued":[54],"functions":[55],"on":[56,69],"Grassmannian.":[59],"Like":[60],"their":[61],"counterparts":[62],"for":[63],"Grassmannian,":[65],"they":[66],"rely":[67],"only":[68],"standard":[70],"numerical":[71],"linear":[72],"algebra":[73],"are":[75],"readily":[76],"computable.":[77]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}