{"id":"https://openalex.org/W2006874591","doi":"https://doi.org/10.1515/cmam-2013-0024","title":"Combined Error Estimates in the Case of Dimension Reduction","display_name":"Combined Error Estimates in the Case of Dimension Reduction","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2006874591","doi":"https://doi.org/10.1515/cmam-2013-0024","mag":"2006874591"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2013-0024","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2013-0024","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035386667","display_name":"Tatiana S. Samrowski","orcid":null},"institutions":[{"id":"https://openalex.org/I858936495","display_name":"ZHAW Zurich University of Applied Sciences","ror":"https://ror.org/05pmsvm27","country_code":"CH","type":"education","lineage":["https://openalex.org/I858936495"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Tatiana Samrowski","raw_affiliation_strings":["1School of Engineering, Zurich University of Applied Sciences, Technikumstrasse 9, 8401 Winterthur, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"1School of Engineering, Zurich University of Applied Sciences, Technikumstrasse 9, 8401 Winterthur, Switzerland","institution_ids":["https://openalex.org/I858936495"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5035386667"],"corresponding_institution_ids":["https://openalex.org/I858936495"],"apc_list":null,"apc_paid":null,"fwci":0.2833,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.58202199,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"14","issue":"1","first_page":"113","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9988999962806702,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9988999962806702,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9944999814033508,"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/T11416","display_name":"Numerical methods for differential equations","score":0.992900013923645,"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/discretization","display_name":"Discretization","score":0.8788671493530273},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7252498865127563},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7159746885299683},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6843289136886597},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5986465215682983},{"id":"https://openalex.org/keywords/discretization-error","display_name":"Discretization error","score":0.5713728666305542},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.503558337688446},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.47764742374420166},{"id":"https://openalex.org/keywords/sufficient-dimension-reduction","display_name":"Sufficient dimension reduction","score":0.47517767548561096},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.466526597738266},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.45393240451812744},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.323722243309021},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32041168212890625},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1191796064376831},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08523029088973999}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8788671493530273},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7252498865127563},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7159746885299683},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6843289136886597},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5986465215682983},{"id":"https://openalex.org/C126148662","wikidata":"https://www.wikidata.org/wiki/Q3890355","display_name":"Discretization error","level":3,"score":0.5713728666305542},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.503558337688446},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.47764742374420166},{"id":"https://openalex.org/C27931671","wikidata":"https://www.wikidata.org/wiki/Q7634497","display_name":"Sufficient dimension reduction","level":3,"score":0.47517767548561096},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.466526597738266},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.45393240451812744},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.323722243309021},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32041168212890625},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1191796064376831},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08523029088973999},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1515/cmam-2013-0024","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2013-0024","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:www.zora.uzh.ch:154571","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401281","display_name":"Zurich Open Repository and Archive (University of Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I202697423","host_organization_name":"University of Zurich","host_organization_lineage":["https://openalex.org/I202697423"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Samrowski, Tatiana (2014). Combined error estimates in the case of dimension reduction. Computational Methods in Applied Mathematics, 14(1):113-134.","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:digitalcollection.zhaw.ch:11475/29622","is_oa":true,"landing_page_url":"https://hdl.handle.net/11475/29622","pdf_url":null,"source":{"id":"https://openalex.org/S4306401811","display_name":"Z\u00fcrcher Hochschule f\u00fcr Angewandte Wissenschaften digital collection (Zurich University of Applied Sciences)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200744771","host_organization_name":"ZHAW Zurich University of Applied Sciences","host_organization_lineage":["https://openalex.org/I200744771"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"doi:10.5167/uzh-154571","is_oa":true,"landing_page_url":"https://doi.org/10.5167/uzh-154571","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"pmh:oai:www.zora.uzh.ch:154571","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401281","display_name":"Zurich Open Repository and Archive (University of Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I202697423","host_organization_name":"University of Zurich","host_organization_lineage":["https://openalex.org/I202697423"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Samrowski, Tatiana (2014). Combined error estimates in the case of dimension reduction. Computational Methods in Applied Mathematics, 14(1):113-134.","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.7400000095367432,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W53139918","https://openalex.org/W174163100","https://openalex.org/W234112145","https://openalex.org/W408406386","https://openalex.org/W1970813923","https://openalex.org/W1997332783","https://openalex.org/W2022208795","https://openalex.org/W2033669462","https://openalex.org/W2084862534","https://openalex.org/W2166941505","https://openalex.org/W4244175368"],"related_works":["https://openalex.org/W2081330222","https://openalex.org/W2085754006","https://openalex.org/W2417586711","https://openalex.org/W3157581885","https://openalex.org/W4213403533","https://openalex.org/W4214791222","https://openalex.org/W2086382493","https://openalex.org/W4291557430","https://openalex.org/W2041896318","https://openalex.org/W2006874591"],"abstract_inverted_index":{"Abstract.":[0],"We":[1],"consider":[2],"the":[3,15,25,54,57,61,70,80,86,110,126],"stationary":[4],"reaction-diffusion":[5],"problem":[6,63],"in":[7,135],"a":[8,49,65,73,106,121,149],"domain":[9],"$\\Omega":[10],"\\subset":[11],"\\mathbb":[12],"{R}^3$":[13],"having":[14],"size":[16],"along":[17,24],"one":[18],"coordinate":[19],"direction":[20],"essentially":[21],"smaller":[22],"than":[23],"others.":[26],"By":[27],"an":[28,139,144,148],"energy":[29],"type":[30],"argumentation,":[31],"different":[32],"simplified":[33],"models":[34],"of":[35,53,60,72,79,88,109,142],"lower":[36],"dimension":[37],"can":[38,132],"be":[39,133],"deduced":[40],"and":[41,64,90,97,129,157],"solved":[42],"numerically.":[43],"For":[44],"these":[45],"models,":[46],"we":[47],"derive":[48],"guaranteed":[50],"upper":[51],"bound":[52],"difference":[55],"between":[56],"exact":[58],"solution":[59,71,146],"original":[62],"three-dimensional":[66],"reconstruction":[67],"generated":[68],"by":[69,105],"dimensionally":[74],"reduced":[75],"problem.":[76],"This":[77],"estimate":[78],"total":[81],"error":[82,114],"is":[83],"determined":[84],"as":[85],"sum":[87],"discretization":[89,101,130],"modeling":[91,128],"errors,":[92],"which":[93],"are":[94,103,116,155],"both":[95],"explicit":[96],"computable.":[98],"The":[99],"corresponding":[100],"errors":[102,131],"estimated":[104],"posteriori":[107],"estimates":[108],"functional":[111],"type.":[112],"Modeling":[113],"majorants":[115],"also":[117],"explicitly":[118],"evaluated.":[119],"Hence,":[120],"numerical":[122],"strategy":[123],"based":[124],"on":[125],"balancing":[127],"derived":[134],"order":[136],"to":[137],"provide":[138],"economical":[140],"way":[141],"getting":[143],"approximate":[145],"with":[147],"priori":[150],"given":[151],"accuracy.":[152],"Numerical":[153],"tests":[154],"presented":[156],"discussed.":[158]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}