{"id":"https://openalex.org/W2793479357","doi":"https://doi.org/10.1007/s10915-018-0689-7","title":"A Globally and Quadratically Convergent Algorithm for Solving Multilinear Systems with $${{\\mathcal {M}}}$$ M -tensors","display_name":"A Globally and Quadratically Convergent Algorithm for Solving Multilinear Systems with $${{\\mathcal {M}}}$$ M -tensors","publication_year":2018,"publication_date":"2018-03-08","ids":{"openalex":"https://openalex.org/W2793479357","doi":"https://doi.org/10.1007/s10915-018-0689-7","mag":"2793479357"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-018-0689-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-018-0689-7","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/20.500.11937/67006","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070555054","display_name":"Hongjin He","orcid":"https://orcid.org/0000-0001-7672-4943"},"institutions":[{"id":"https://openalex.org/I50760025","display_name":"Hangzhou Dianzi University","ror":"https://ror.org/0576gt767","country_code":"CN","type":"education","lineage":["https://openalex.org/I50760025"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongjin He","raw_affiliation_strings":["Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China","institution_ids":["https://openalex.org/I50760025"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101911109","display_name":"Chen Ling","orcid":"https://orcid.org/0000-0001-9103-0501"},"institutions":[{"id":"https://openalex.org/I50760025","display_name":"Hangzhou Dianzi University","ror":"https://ror.org/0576gt767","country_code":"CN","type":"education","lineage":["https://openalex.org/I50760025"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen Ling","raw_affiliation_strings":["Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China","institution_ids":["https://openalex.org/I50760025"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011886900","display_name":"Liqun Qi","orcid":"https://orcid.org/0000-0002-1112-5250"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Liqun Qi","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037628561","display_name":"Guanglu Zhou","orcid":"https://orcid.org/0000-0002-8811-885X"},"institutions":[{"id":"https://openalex.org/I205640436","display_name":"Curtin University","ror":"https://ror.org/02n415q13","country_code":"AU","type":"education","lineage":["https://openalex.org/I205640436"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Guanglu Zhou","raw_affiliation_strings":["Department of Mathematics and Statistics, Curtin University, Perth, WA, Australia"],"raw_orcid":"https://orcid.org/0000-0002-8811-885X","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Curtin University, Perth, WA, Australia","institution_ids":["https://openalex.org/I205640436"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5037628561"],"corresponding_institution_ids":["https://openalex.org/I205640436"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":4.8976,"has_fulltext":true,"cited_by_count":67,"citation_normalized_percentile":{"value":0.97131148,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"76","issue":"3","first_page":"1718","last_page":"1741"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/T12303","display_name":"Tensor decomposition and applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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":0.932699978351593,"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/multilinear-map","display_name":"Multilinear map","score":0.9686157703399658},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8024914860725403},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.6243085265159607},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5936948657035828},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5427915453910828},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5211320519447327},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4753146767616272},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4502869248390198},{"id":"https://openalex.org/keywords/quadratic-growth","display_name":"Quadratic growth","score":0.42819908261299133},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4223247766494751},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41144293546676636},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37405019998550415},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33289575576782227},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32739585638046265},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.12960368394851685},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09925580024719238},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09389761090278625}],"concepts":[{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.9686157703399658},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8024914860725403},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6243085265159607},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5936948657035828},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5427915453910828},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5211320519447327},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4753146767616272},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4502869248390198},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.42819908261299133},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4223247766494751},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41144293546676636},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37405019998550415},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33289575576782227},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32739585638046265},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.12960368394851685},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09925580024719238},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09389761090278625},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10915-018-0689-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-018-0689-7","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:espace.curtin.edu.au:20.500.11937/67006","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11937/67006","pdf_url":"http://hdl.handle.net/20.500.11937/67006","source":{"id":"https://openalex.org/S4306401790","display_name":"eSpace (Curtin University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205640436","host_organization_name":"Curtin University","host_organization_lineage":["https://openalex.org/I205640436"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/78265","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/78265","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal/Magazine Article"}],"best_oa_location":{"id":"pmh:oai:espace.curtin.edu.au:20.500.11937/67006","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11937/67006","pdf_url":"http://hdl.handle.net/20.500.11937/67006","source":{"id":"https://openalex.org/S4306401790","display_name":"eSpace (Curtin University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205640436","host_organization_name":"Curtin University","host_organization_lineage":["https://openalex.org/I205640436"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G110287858","display_name":null,"funder_award_id":"15302114","funder_id":"https://openalex.org/F4320322598","funder_display_name":"Hong Kong Polytechnic University"},{"id":"https://openalex.org/G1265713254","display_name":null,"funder_award_id":"LY17A010028","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"},{"id":"https://openalex.org/G1732053830","display_name":null,"funder_award_id":"501913","funder_id":"https://openalex.org/F4320322598","funder_display_name":"Hong Kong Polytechnic University"},{"id":"https://openalex.org/G2404516597","display_name":null,"funder_award_id":"11571087,11771113","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3328376380","display_name":null,"funder_award_id":"502111","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4111498857","display_name":null,"funder_award_id":"11571087","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4350608149","display_name":null,"funder_award_id":"LZ14A010003","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"},{"id":"https://openalex.org/G4456855145","display_name":null,"funder_award_id":"11771113","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4478465004","display_name":null,"funder_award_id":"502111","funder_id":"https://openalex.org/F4320322598","funder_display_name":"Hong Kong Polytechnic University"},{"id":"https://openalex.org/G4850618809","display_name":null,"funder_award_id":"11601261","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5823696539","display_name":null,"funder_award_id":"501212","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7860316853","display_name":null,"funder_award_id":"LZ14A010003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8070831889","display_name":null,"funder_award_id":"501913","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8304336271","display_name":null,"funder_award_id":"501212","funder_id":"https://openalex.org/F4320322598","funder_display_name":"Hong Kong Polytechnic University"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322598","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98"},{"id":"https://openalex.org/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2793479357.pdf","grobid_xml":"https://content.openalex.org/works/W2793479357.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1500921805","https://openalex.org/W1543439990","https://openalex.org/W1560867458","https://openalex.org/W1951162345","https://openalex.org/W1964200011","https://openalex.org/W1968373943","https://openalex.org/W1974018266","https://openalex.org/W1981220107","https://openalex.org/W2012593053","https://openalex.org/W2023092664","https://openalex.org/W2044382581","https://openalex.org/W2048636460","https://openalex.org/W2057953211","https://openalex.org/W2071491310","https://openalex.org/W2090208105","https://openalex.org/W2120001551","https://openalex.org/W2124664178","https://openalex.org/W2222111999","https://openalex.org/W2582681631","https://openalex.org/W2609276162","https://openalex.org/W2766794278","https://openalex.org/W2767311547","https://openalex.org/W2785941732","https://openalex.org/W3119264343","https://openalex.org/W4245490374","https://openalex.org/W4295016751","https://openalex.org/W4301791716"],"related_works":["https://openalex.org/W3098916583","https://openalex.org/W2146655208","https://openalex.org/W2922481674","https://openalex.org/W3193555930","https://openalex.org/W1572092093","https://openalex.org/W1570745949","https://openalex.org/W2893527900","https://openalex.org/W3043534693","https://openalex.org/W3177385724","https://openalex.org/W2535617683"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":17},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2018-03-29T00:00:00"}