{"id":"https://openalex.org/W2112160616","doi":"https://doi.org/10.1007/s10208-013-9187-3","title":"Adaptive Near-Optimal Rank Tensor Approximation for High-Dimensional Operator Equations","display_name":"Adaptive Near-Optimal Rank Tensor Approximation for High-Dimensional Operator Equations","publication_year":2014,"publication_date":"2014-03-13","ids":{"openalex":"https://openalex.org/W2112160616","doi":"https://doi.org/10.1007/s10208-013-9187-3","mag":"2112160616"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-013-9187-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-013-9187-3","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1304.7796","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Markus Bachmayr","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Markus Bachmayr","raw_affiliation_strings":["Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH Aachen, Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH Aachen, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":null,"display_name":"Wolfgang Dahmen","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Wolfgang Dahmen","raw_affiliation_strings":["Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH Aachen, Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH Aachen, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I887968799"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.8826,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.83905579,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"15","issue":"4","first_page":"839","last_page":"898"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.8141000270843506,"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":0.8141000270843506,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.0729999989271164,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.042399998754262924,"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/convergence","display_name":"Convergence (economics)","score":0.5839999914169312},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5605000257492065},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5099999904632568},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.453900009393692},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.41659998893737793},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.39750000834465027},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.3930000066757202},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.39239999651908875},{"id":"https://openalex.org/keywords/numerical-approximation","display_name":"Numerical approximation","score":0.3849000036716461}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7735000252723694},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5839999914169312},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5605000257492065},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5099999904632568},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49070000648498535},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.453900009393692},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.41659998893737793},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.39750000834465027},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3930000066757202},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.39239999651908875},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.3849000036716461},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3725999891757965},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.3709999918937683},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3610000014305115},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.3492000102996826},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.3391000032424927},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.32829999923706055},{"id":"https://openalex.org/C2987355758","wikidata":"https://www.wikidata.org/wiki/Q25037251","display_name":"Operator splitting","level":2,"score":0.3118000030517578},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3093999922275543},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.3068999946117401},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.29989999532699585},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C2776003309","wikidata":"https://www.wikidata.org/wiki/Q1988072","display_name":"Adaptive algorithm","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.26159998774528503},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10208-013-9187-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-013-9187-3","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1304.7796","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.7796","pdf_url":"https://arxiv.org/pdf/1304.7796","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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1304.7796","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.7796","pdf_url":"https://arxiv.org/pdf/1304.7796","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W50417968","https://openalex.org/W1504748373","https://openalex.org/W1963826206","https://openalex.org/W1967077133","https://openalex.org/W1967402714","https://openalex.org/W1975206377","https://openalex.org/W1980428773","https://openalex.org/W1993482030","https://openalex.org/W1995406764","https://openalex.org/W2001292054","https://openalex.org/W2013912476","https://openalex.org/W2024165284","https://openalex.org/W2034801304","https://openalex.org/W2038198231","https://openalex.org/W2048834141","https://openalex.org/W2056404710","https://openalex.org/W2058288586","https://openalex.org/W2062064231","https://openalex.org/W2073469810","https://openalex.org/W2075646404","https://openalex.org/W2079275676","https://openalex.org/W2084087478","https://openalex.org/W2084617396","https://openalex.org/W2088025933","https://openalex.org/W2088739747","https://openalex.org/W2100917607","https://openalex.org/W2115566547","https://openalex.org/W2132267493","https://openalex.org/W2136128169","https://openalex.org/W2160251536","https://openalex.org/W2330159389","https://openalex.org/W2963858059","https://openalex.org/W6603592625"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}