{"id":"https://openalex.org/W2883042798","doi":"https://doi.org/10.3390/axioms7030051","title":"A Gradient System for Low Rank Matrix Completion","display_name":"A Gradient System for Low Rank Matrix Completion","publication_year":2018,"publication_date":"2018-07-24","ids":{"openalex":"https://openalex.org/W2883042798","doi":"https://doi.org/10.3390/axioms7030051","mag":"2883042798"},"language":"en","primary_location":{"id":"doi:10.3390/axioms7030051","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms7030051","pdf_url":"https://www.mdpi.com/2075-1680/7/3/51/pdf?version=1532431423","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/7/3/51/pdf?version=1532431423","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017254386","display_name":"Carmela Scalone","orcid":null},"institutions":[{"id":"https://openalex.org/I26415053","display_name":"University of L'Aquila","ror":"https://ror.org/01j9p1r26","country_code":"IT","type":"education","lineage":["https://openalex.org/I26415053"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Carmela Scalone","raw_affiliation_strings":["Dipartimento di Ingegneria e Scienze dell\u2019Informazione e Matematica (DISIM), Universit\u00e0 dell\u2019Aquila, via Vetoio 1, 67100 L\u2019Aquila, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria e Scienze dell\u2019Informazione e Matematica (DISIM), Universit\u00e0 dell\u2019Aquila, via Vetoio 1, 67100 L\u2019Aquila, Italy","institution_ids":["https://openalex.org/I26415053"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030219464","display_name":"Nicola Guglielmi","orcid":"https://orcid.org/0000-0003-3795-5225"},"institutions":[{"id":"https://openalex.org/I4210150763","display_name":"Gran Sasso Science Institute","ror":"https://ror.org/043qcb444","country_code":"IT","type":"education","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210150763"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Nicola Guglielmi","raw_affiliation_strings":["Section of Mathematics, Gran Sasso Science Institute, via Crispi 7, 67100 L\u2019Aquila, Italy","Section of Mathematics, Gran Sasso Science Institute, via Crispi 7, 67100 L'Aquila, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Section of Mathematics, Gran Sasso Science Institute, via Crispi 7, 67100 L\u2019Aquila, Italy","institution_ids":["https://openalex.org/I4210150763"]},{"raw_affiliation_string":"Section of Mathematics, Gran Sasso Science Institute, via Crispi 7, 67100 L'Aquila, Italy","institution_ids":["https://openalex.org/I4210150763"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017254386"],"corresponding_institution_ids":["https://openalex.org/I26415053"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.8326,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.70360176,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"7","issue":"3","first_page":"51","last_page":"51"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"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":0.9973999857902527,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9904999732971191,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.7383618354797363},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.7361053824424744},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.7024574875831604},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.7015579342842102},{"id":"https://openalex.org/keywords/matrix-completion","display_name":"Matrix completion","score":0.685248076915741},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6221594214439392},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.4939196705818176},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4111369550228119},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3723059594631195},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3384701609611511},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.25676172971725464},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.10616952180862427},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09824585914611816},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.07293260097503662},{"id":"https://openalex.org/keywords/computational-chemistry","display_name":"Computational chemistry","score":0.05298295617103577},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.046989649534225464}],"concepts":[{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.7383618354797363},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7361053824424744},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.7024574875831604},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.7015579342842102},{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.685248076915741},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6221594214439392},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.4939196705818176},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4111369550228119},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3723059594631195},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3384701609611511},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25676172971725464},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.10616952180862427},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09824585914611816},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.07293260097503662},{"id":"https://openalex.org/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","level":1,"score":0.05298295617103577},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.046989649534225464},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms7030051","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms7030051","pdf_url":"https://www.mdpi.com/2075-1680/7/3/51/pdf?version=1532431423","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:715e4e11f59e4b77aae412cde12c0642","is_oa":true,"landing_page_url":"https://doaj.org/article/715e4e11f59e4b77aae412cde12c0642","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 7, Iss 3, p 51 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/7/3/51/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms7030051","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms7030051","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms7030051","pdf_url":"https://www.mdpi.com/2075-1680/7/3/51/pdf?version=1532431423","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2883042798.pdf","grobid_xml":"https://content.openalex.org/works/W2883042798.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1966553486","https://openalex.org/W1972112356","https://openalex.org/W2000157792","https://openalex.org/W2001187684","https://openalex.org/W2006017464","https://openalex.org/W2027924293","https://openalex.org/W2032024719","https://openalex.org/W2047071281","https://openalex.org/W2058078260","https://openalex.org/W2096434207","https://openalex.org/W2103972604","https://openalex.org/W2105936267","https://openalex.org/W2123688186","https://openalex.org/W2150386905","https://openalex.org/W2152279941","https://openalex.org/W2162171343","https://openalex.org/W2266965707","https://openalex.org/W2397487909","https://openalex.org/W2597503451","https://openalex.org/W2611328865","https://openalex.org/W2741550485","https://openalex.org/W2789846523","https://openalex.org/W3103516706","https://openalex.org/W4300791824","https://openalex.org/W6650231177"],"related_works":["https://openalex.org/W2964006653","https://openalex.org/W2788826952","https://openalex.org/W4302315572","https://openalex.org/W2084983808","https://openalex.org/W2325477568","https://openalex.org/W1991825408","https://openalex.org/W3144354057","https://openalex.org/W4318564253","https://openalex.org/W1969698720","https://openalex.org/W1507830821"],"abstract_inverted_index":{"In":[0],"this":[1,65],"article":[2],"we":[3],"present":[4],"and":[5,38,100],"discuss":[6],"a":[7,19,24,74,97],"two":[8],"step":[9],"methodology":[10],"to":[11,36,47,86],"find":[12],"the":[13,29,34,42,50,55,62,71,94,104,108],"closest":[14,43],"low":[15],"rank":[16,35],"completion":[17],"of":[18,32,64,70,73,78],"sparse":[20,26],"large":[21,25],"matrix.":[22],"Given":[23],"matrix":[27,45,66,79],"M,":[28,48],"method":[30,95],"consists":[31,69],"fixing":[33],"r":[37],"then":[39],"looking":[40],"for":[41],"rank-r":[44],"X":[46],"where":[49],"distance":[51],"is":[52,101],"measured":[53],"in":[54,61,107],"Frobenius":[56],"norm.":[57],"A":[58],"key":[59],"element":[60],"solution":[63],"nearness":[67],"problem":[68],"use":[72],"constrained":[75],"gradient":[76],"system":[77],"differential":[80],"equations.":[81],"The":[82],"obtained":[83,88],"results,":[84],"compared":[85],"those":[87],"by":[89],"different":[90],"approaches":[91],"show":[92],"that":[93],"has":[96],"correct":[98],"behaviour":[99],"competitive":[102],"with":[103],"ones":[105],"available":[106],"literature.":[109]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}