{"id":"https://openalex.org/W3161684506","doi":"https://doi.org/10.31577/cai_2020_6_1203","title":"Error Analysis of the Cholesky QR-Based Block Orthogonalization Process for the One-Sided Block Jacobi SVD Algorithm","display_name":"Error Analysis of the Cholesky QR-Based Block Orthogonalization Process for the One-Sided Block Jacobi SVD Algorithm","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3161684506","doi":"https://doi.org/10.31577/cai_2020_6_1203","mag":"3161684506"},"language":"en","primary_location":{"id":"doi:10.31577/cai_2020_6_1203","is_oa":true,"landing_page_url":"https://doi.org/10.31577/cai_2020_6_1203","pdf_url":null,"source":{"id":"https://openalex.org/S4210200093","display_name":"Computing and Informatics","issn_l":"1335-9150","issn":["1335-9150","2585-8807"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing and Informatics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.31577/cai_2020_6_1203","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071413651","display_name":"Shuhei Kudo","orcid":"https://orcid.org/0009-0003-7168-5764"},"institutions":[{"id":"https://openalex.org/I4210129730","display_name":"RIKEN Center for Computational Science","ror":"https://ror.org/03r519674","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210129730"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Shuhei Kudo","raw_affiliation_strings":["RIKEN Center for Computational Science, 7-1-26, Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan"],"affiliations":[{"raw_affiliation_string":"RIKEN Center for Computational Science, 7-1-26, Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan","institution_ids":["https://openalex.org/I4210129730"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103155193","display_name":"Yusaku Yamamoto","orcid":"https://orcid.org/0000-0001-5682-3434"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yusaku Yamamoto","raw_affiliation_strings":["Department of Communication Engineering and Informatics, The University of Electro-Communications, 1-5-1, Chofugaoka, Chofu, Tokyo, 182-8585, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Communication Engineering and Informatics, The University of Electro-Communications, 1-5-1, Chofugaoka, Chofu, Tokyo, 182-8585, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086152822","display_name":"Toshiyuki Imamura","orcid":"https://orcid.org/0000-0003-1601-9710"},"institutions":[{"id":"https://openalex.org/I4210129730","display_name":"RIKEN Center for Computational Science","ror":"https://ror.org/03r519674","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210129730"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Toshiyuki Imamura","raw_affiliation_strings":["RIKEN Center for Computational Science, 7-1-26, Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan"],"affiliations":[{"raw_affiliation_string":"RIKEN Center for Computational Science, 7-1-26, Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan","institution_ids":["https://openalex.org/I4210129730"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071413651"],"corresponding_institution_ids":["https://openalex.org/I4210129730"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.27607076,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"39","issue":"6","first_page":"1203","last_page":"1228"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9950000047683716,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9950000047683716,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9944999814033508,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9736999869346619,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cholesky-decomposition","display_name":"Cholesky decomposition","score":0.9574110507965088},{"id":"https://openalex.org/keywords/orthogonalization","display_name":"Orthogonalization","score":0.8501839637756348},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.8456284999847412},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.6956038475036621},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.674208402633667},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6646848320960999},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.5220651030540466},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5192537307739258},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.513076663017273},{"id":"https://openalex.org/keywords/minimum-degree-algorithm","display_name":"Minimum degree algorithm","score":0.42283183336257935},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4013330638408661},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.34473681449890137},{"id":"https://openalex.org/keywords/incomplete-cholesky-factorization","display_name":"Incomplete Cholesky factorization","score":0.22479015588760376},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12332934141159058},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.060214996337890625}],"concepts":[{"id":"https://openalex.org/C34727166","wikidata":"https://www.wikidata.org/wiki/Q515375","display_name":"Cholesky decomposition","level":3,"score":0.9574110507965088},{"id":"https://openalex.org/C47559304","wikidata":"https://www.wikidata.org/wiki/Q1702189","display_name":"Orthogonalization","level":2,"score":0.8501839637756348},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.8456284999847412},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.6956038475036621},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.674208402633667},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6646848320960999},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.5220651030540466},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5192537307739258},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.513076663017273},{"id":"https://openalex.org/C46085209","wikidata":"https://www.wikidata.org/wiki/Q17098969","display_name":"Minimum degree algorithm","level":5,"score":0.42283183336257935},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4013330638408661},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.34473681449890137},{"id":"https://openalex.org/C44363057","wikidata":"https://www.wikidata.org/wiki/Q6015160","display_name":"Incomplete Cholesky factorization","level":4,"score":0.22479015588760376},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12332934141159058},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.060214996337890625},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.31577/cai_2020_6_1203","is_oa":true,"landing_page_url":"https://doi.org/10.31577/cai_2020_6_1203","pdf_url":null,"source":{"id":"https://openalex.org/S4210200093","display_name":"Computing and Informatics","issn_l":"1335-9150","issn":["1335-9150","2585-8807"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing and Informatics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.31577/cai_2020_6_1203","is_oa":true,"landing_page_url":"https://doi.org/10.31577/cai_2020_6_1203","pdf_url":null,"source":{"id":"https://openalex.org/S4210200093","display_name":"Computing and Informatics","issn_l":"1335-9150","issn":["1335-9150","2585-8807"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing and Informatics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1483820693","https://openalex.org/W1659328298","https://openalex.org/W1984456322","https://openalex.org/W2002051125","https://openalex.org/W2003670573","https://openalex.org/W2020804487","https://openalex.org/W2020828929","https://openalex.org/W2023467209","https://openalex.org/W2031724759","https://openalex.org/W2054260755","https://openalex.org/W2058443643","https://openalex.org/W2059586807","https://openalex.org/W2072633114","https://openalex.org/W2093637157","https://openalex.org/W2107344003","https://openalex.org/W2117026915","https://openalex.org/W2470554868","https://openalex.org/W2561148045","https://openalex.org/W2604250686","https://openalex.org/W2765309601","https://openalex.org/W2900234561"],"related_works":["https://openalex.org/W2982181895","https://openalex.org/W2035803264","https://openalex.org/W2039527536","https://openalex.org/W3035209767","https://openalex.org/W4306891336","https://openalex.org/W2412724763","https://openalex.org/W2135765421","https://openalex.org/W1966820346","https://openalex.org/W2739115385","https://openalex.org/W4293690747"],"abstract_inverted_index":{"The":[0,21],"one-sided":[1],"block":[2,31,41],"Jacobi":[3],"method":[4],"(OSBJ)":[5],"has":[6],"attracted":[7],"attention":[8],"as":[9],"a":[10,29,81,85,105,132],"fast":[11],"and":[12,51,74,113,116],"accurate":[13],"algorithm":[14],"for":[15,47,135],"the":[16,37,58,66,71,92,96,110,124,137,142],"singular":[17],"value":[18],"decomposition":[19],"(SVD).":[20],"computational":[22],"kernel":[23],"of":[24,28,39,95,109],"OSBJ":[25,143],"is":[26,63,70,80],"orthogonalization":[27],"column":[30],"pair,":[32],"which":[33,62],"amounts":[34],"to":[35,122],"computing":[36],"SVD":[38,126],"this":[40,48,101],"pair.":[42],"Hari":[43],"proposes":[44],"three":[45],"methods":[46],"partial":[49,125],"SVD,":[50],"we":[52,103],"found":[53],"through":[54],"numerical":[55],"experiments":[56],"that":[57],"variant":[59,73,112,139],"named":[60],"\"V2\",":[61],"based":[64],"on":[65],"Cholesky":[67,97],"QR":[68,98],"method,":[69],"fastest":[72],"achieves":[75],"satisfactory":[76],"accuracy.":[77],"While":[78],"it":[79,88,118],"good":[82],"news":[83],"from":[84],"practical":[86],"viewpoint,":[87],"seems":[89],"strange":[90],"considering":[91],"well-known":[93],"instability":[94],"method.":[99,144],"In":[100],"paper,":[102],"perform":[104],"detailed":[106],"error":[107],"analysis":[108],"V2":[111,138],"explain":[114],"why":[115],"when":[117],"can":[119],"be":[120],"used":[121],"compute":[123],"accurately.":[127],"Thus,":[128],"our":[129],"results":[130],"provide":[131],"theoretical":[133],"support":[134],"using":[136],"safely":[140],"in":[141]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-29T08:15:47.926485","created_date":"2025-10-10T00:00:00"}
