{"id":"https://openalex.org/W2752783311","doi":"https://doi.org/10.1137/17m1146889","title":"Time Integration of Rank-Constrained Tucker Tensors","display_name":"Time Integration of Rank-Constrained Tucker Tensors","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2752783311","doi":"https://doi.org/10.1137/17m1146889","mag":"2752783311"},"language":"en","primary_location":{"id":"doi:10.1137/17m1146889","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1146889","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1709.02594","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065792988","display_name":"Christian Lubich","orcid":"https://orcid.org/0000-0003-0105-4927"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Christian Lubich","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039297086","display_name":"Bart Vandereycken","orcid":"https://orcid.org/0000-0002-6501-816X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bart Vandereycken","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078166905","display_name":"Hanna Walach","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hanna Walach","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5065792988"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5047,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.54258242,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"56","issue":"3","first_page":"1273","last_page":"1290"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9807999730110168,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9593999981880188,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.8402721285820007},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.7750863432884216},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.7624026536941528},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.660895824432373},{"id":"https://openalex.org/keywords/projector","display_name":"Projector","score":0.6447914838790894},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4507260322570801},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42917048931121826},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.336531400680542},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33466655015945435},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19312644004821777},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09815549850463867}],"concepts":[{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.8402721285820007},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.7750863432884216},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7624026536941528},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.660895824432373},{"id":"https://openalex.org/C2776865275","wikidata":"https://www.wikidata.org/wiki/Q311666","display_name":"Projector","level":2,"score":0.6447914838790894},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4507260322570801},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42917048931121826},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.336531400680542},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33466655015945435},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19312644004821777},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09815549850463867},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/17m1146889","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1146889","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1709.02594","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.02594","pdf_url":"https://arxiv.org/pdf/1709.02594","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2752783311","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1709.02594.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1709.02594","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1709.02594","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1709.02594","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.02594","pdf_url":"https://arxiv.org/pdf/1709.02594","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8562152207","display_name":null,"funder_award_id":"GRK 1838","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2752783311.pdf","grobid_xml":"https://content.openalex.org/works/W2752783311.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W50417968","https://openalex.org/W434969687","https://openalex.org/W1580989833","https://openalex.org/W1972710290","https://openalex.org/W2013912476","https://openalex.org/W2024165284","https://openalex.org/W2049202763","https://openalex.org/W2051456448","https://openalex.org/W2096434207","https://openalex.org/W2102688209","https://openalex.org/W2115402677","https://openalex.org/W2118115288","https://openalex.org/W2491218394","https://openalex.org/W2610547747","https://openalex.org/W2884158030","https://openalex.org/W3104980255"],"related_works":["https://openalex.org/W3003761894","https://openalex.org/W6878287","https://openalex.org/W2530345780","https://openalex.org/W2147466962","https://openalex.org/W183668700","https://openalex.org/W3199341759","https://openalex.org/W2619429851","https://openalex.org/W3030515421","https://openalex.org/W3211591805","https://openalex.org/W2031764552","https://openalex.org/W2810771934","https://openalex.org/W3009651996","https://openalex.org/W2008657736","https://openalex.org/W2040932470","https://openalex.org/W3005149638","https://openalex.org/W3178375239","https://openalex.org/W2601861499","https://openalex.org/W2073726461","https://openalex.org/W2142707586","https://openalex.org/W2988350657"],"abstract_inverted_index":{"Dynamical":[0],"low-rank":[1,47],"approximation":[2,48],"in":[3,81,114],"the":[4,19,41,59,70,86,95,108,115],"Tucker":[5,33,52,92],"tensor":[6,15,75,116,126],"format":[7],"of":[8,14,21,49,94,110],"given":[9,96],"large":[10],"time-dependent":[11,91],"tensors":[12,34,53,93],"and":[13,37,54,125],"differential":[16],"equations":[17],"is":[18,35,55,65,101],"subject":[20],"this":[22],"paper.":[23],"In":[24],"particular,":[25],"a":[26,82],"discrete":[27],"time":[28],"integration":[29],"method":[30],"for":[31,45],"rank-constrained":[32],"presented":[36],"analyzed.":[38],"It":[39,84],"extends":[40],"known":[42],"projector-splitting":[43,72],"integrator":[44,64,73,100],"dynamical":[46],"matrices":[50],"to":[51,57,74,104,107],"shown":[56,103],"inherit":[58],"same":[60],"favorable":[61],"properties.":[62],"The":[63,99],"based":[66],"on":[67],"iteratively":[68],"applying":[69],"matrix":[71],"unfoldings":[76],"but":[77],"with":[78,120],"inexact":[79],"solution":[80],"substep.":[83],"has":[85],"property":[87],"that":[88],"it":[89],"reconstructs":[90],"rank":[97],"exactly.":[98],"also":[102],"be":[105],"robust":[106],"presence":[109],"small":[111],"singular":[112],"values":[113],"unfoldings.":[117],"Numerical":[118],"examples":[119],"problems":[121],"from":[122],"quantum":[123],"dynamics":[124],"optimization":[127],"methods":[128],"illustrate":[129],"our":[130],"theoretical":[131],"results.":[132]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}