{"id":"https://openalex.org/W1999498154","doi":"https://doi.org/10.1007/s00211-011-0424-x","title":"Balanced POD for model reduction of linear PDE systems: convergence theory","display_name":"Balanced POD for model reduction of linear PDE systems: convergence theory","publication_year":2011,"publication_date":"2011-11-05","ids":{"openalex":"https://openalex.org/W1999498154","doi":"https://doi.org/10.1007/s00211-011-0424-x","mag":"1999498154"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-011-0424-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-011-0424-x","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065565731","display_name":"John R. Singler","orcid":"https://orcid.org/0000-0002-5415-8386"},"institutions":[{"id":"https://openalex.org/I20382870","display_name":"Missouri University of Science and Technology","ror":"https://ror.org/00scwqd12","country_code":"US","type":"education","lineage":["https://openalex.org/I20382870"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"John R. Singler","raw_affiliation_strings":["Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, 65409-0020, USA","Missouri University of Science and Technology, Department of Mathematics and Statistics, 65409-0020, Rolla, MO, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, 65409-0020, USA","institution_ids":["https://openalex.org/I20382870"]},{"raw_affiliation_string":"Missouri University of Science and Technology, Department of Mathematics and Statistics, 65409-0020, Rolla, MO, USA#TAB#","institution_ids":["https://openalex.org/I20382870"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065565731"],"corresponding_institution_ids":["https://openalex.org/I20382870"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.9545,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.85977179,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"121","issue":"1","first_page":"127","last_page":"164"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":1.0,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.989300012588501,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8220202326774597},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5788581371307373},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.525631844997406},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5156225562095642},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.48582741618156433},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4734646677970886},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4703417420387268},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4467615485191345},{"id":"https://openalex.org/keywords/minimal-realization","display_name":"Minimal realization","score":0.4324924051761627},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4104435443878174},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.34750014543533325},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29964548349380493}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8220202326774597},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5788581371307373},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.525631844997406},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5156225562095642},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48582741618156433},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4734646677970886},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4703417420387268},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4467615485191345},{"id":"https://openalex.org/C205609532","wikidata":"https://www.wikidata.org/wiki/Q770324","display_name":"Minimal realization","level":3,"score":0.4324924051761627},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4104435443878174},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.34750014543533325},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29964548349380493},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00211-011-0424-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-011-0424-x","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W163224475","https://openalex.org/W297328598","https://openalex.org/W601797399","https://openalex.org/W1413841356","https://openalex.org/W1492498476","https://openalex.org/W1498075298","https://openalex.org/W1509296830","https://openalex.org/W1527296550","https://openalex.org/W1535905504","https://openalex.org/W1537906002","https://openalex.org/W1538055196","https://openalex.org/W1538686203","https://openalex.org/W1551480811","https://openalex.org/W1577805774","https://openalex.org/W1579236455","https://openalex.org/W1601728065","https://openalex.org/W1607896190","https://openalex.org/W1633869374","https://openalex.org/W1868559974","https://openalex.org/W1971630880","https://openalex.org/W1973337814","https://openalex.org/W1982213859","https://openalex.org/W1984396502","https://openalex.org/W1989951672","https://openalex.org/W1994251552","https://openalex.org/W2007581597","https://openalex.org/W2017745440","https://openalex.org/W2046304197","https://openalex.org/W2059316647","https://openalex.org/W2064733273","https://openalex.org/W2065313971","https://openalex.org/W2071861954","https://openalex.org/W2128713754","https://openalex.org/W2128953295","https://openalex.org/W2152741992","https://openalex.org/W2156830882","https://openalex.org/W2160835412","https://openalex.org/W2360038112","https://openalex.org/W2945490868","https://openalex.org/W3100312030","https://openalex.org/W3105504410","https://openalex.org/W3195133498","https://openalex.org/W3216034703","https://openalex.org/W4206263661","https://openalex.org/W4239688777","https://openalex.org/W4256195296","https://openalex.org/W4292399988"],"related_works":["https://openalex.org/W2999616507","https://openalex.org/W4323927134","https://openalex.org/W3164276969","https://openalex.org/W4290705296","https://openalex.org/W2561514193","https://openalex.org/W2115895183","https://openalex.org/W2329896581","https://openalex.org/W2468907551","https://openalex.org/W2505066019","https://openalex.org/W119222235"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}