{"id":"https://openalex.org/W1959436232","doi":"https://doi.org/10.1090/mcom/3209","title":"A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems","display_name":"A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems","publication_year":2016,"publication_date":"2016-09-21","ids":{"openalex":"https://openalex.org/W1959436232","doi":"https://doi.org/10.1090/mcom/3209","mag":"1959436232"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3209","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3209","pdf_url":"https://www.ams.org/mcom/2018-87-309/S0025-5718-2017-03209-9/S0025-5718-2017-03209-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2018-87-309/S0025-5718-2017-03209-9/S0025-5718-2017-03209-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001768471","display_name":"Simone Brugiapaglia","orcid":"https://orcid.org/0000-0003-1927-8232"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Simone Brugiapaglia","raw_affiliation_strings":["MOX, Dipartimento di Matematica, Politecnico di Milano, 20133, Milano, Italy"],"affiliations":[{"raw_affiliation_string":"MOX, Dipartimento di Matematica, Politecnico di Milano, 20133, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043766972","display_name":"Fabio Nobile","orcid":"https://orcid.org/0000-0002-8130-0114"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Fabio Nobile","raw_affiliation_strings":["MATHICSE-CSQI, \u00c3\u0089cole Polytechnique F\u00c3\u00a9d\u00c3\u00a9rale de Lausanne, Lausanne, CH-1015, Switzerland","MATHICSE-CSQI, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne CH-1015, Switzerland"],"affiliations":[{"raw_affiliation_string":"MATHICSE-CSQI, \u00c3\u0089cole Polytechnique F\u00c3\u00a9d\u00c3\u00a9rale de Lausanne, Lausanne, CH-1015, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"MATHICSE-CSQI, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne CH-1015, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043025876","display_name":"Stefano Micheletti","orcid":"https://orcid.org/0000-0001-6559-299X"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Stefano Micheletti","raw_affiliation_strings":["MOX, Dipartimento di Matematica, Politecnico di Milano, 20133, Milano, Italy"],"affiliations":[{"raw_affiliation_string":"MOX, Dipartimento di Matematica, Politecnico di Milano, 20133, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001789052","display_name":"Simona Perotto","orcid":"https://orcid.org/0000-0003-2994-7516"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Simona Perotto","raw_affiliation_strings":["MOX, Dipartimento di Matematica, Politecnico di Milano, 20133, Milano, Italy"],"affiliations":[{"raw_affiliation_string":"MOX, Dipartimento di Matematica, Politecnico di Milano, 20133, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5001768471"],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":null,"apc_paid":null,"fwci":1.1714,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.82896519,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"87","issue":"309","first_page":"1","last_page":"38"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9991999864578247,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8296538591384888},{"id":"https://openalex.org/keywords/restricted-isometry-property","display_name":"Restricted isometry property","score":0.8001580238342285},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.6713003516197205},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5509008765220642},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.549642026424408},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5324656963348389},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5111978650093079},{"id":"https://openalex.org/keywords/advection","display_name":"Advection","score":0.4251352846622467},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36076679825782776},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23228856921195984}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8296538591384888},{"id":"https://openalex.org/C17902559","wikidata":"https://www.wikidata.org/wiki/Q17099734","display_name":"Restricted isometry property","level":3,"score":0.8001580238342285},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.6713003516197205},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5509008765220642},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.549642026424408},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5324656963348389},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5111978650093079},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.4251352846622467},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36076679825782776},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23228856921195984},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/mcom/3209","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3209","pdf_url":"https://www.ams.org/mcom/2018-87-309/S0025-5718-2017-03209-9/S0025-5718-2017-03209-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:211261","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/211261","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"pmh:oai:infoscience.tind.io:211261","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/record/211261/files/2018_Brugiapaglia_Nobile_Micheletti_Perotto_MC_CORSING.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"},{"id":"pmh:oai:re.public.polimi.it:11311/1051439","is_oa":true,"landing_page_url":"http://hdl.handle.net/11311/1051439","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1090/mcom/3209","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3209","pdf_url":"https://www.ams.org/mcom/2018-87-309/S0025-5718-2017-03209-9/S0025-5718-2017-03209-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1959436232.pdf","grobid_xml":"https://content.openalex.org/works/W1959436232.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W143004564","https://openalex.org/W184188664","https://openalex.org/W653136046","https://openalex.org/W1166999322","https://openalex.org/W1202875439","https://openalex.org/W1575470334","https://openalex.org/W1601728065","https://openalex.org/W1652045230","https://openalex.org/W1963563982","https://openalex.org/W1967011851","https://openalex.org/W1977520307","https://openalex.org/W1980635834","https://openalex.org/W1986931325","https://openalex.org/W2016823491","https://openalex.org/W2026679679","https://openalex.org/W2028781966","https://openalex.org/W2031978570","https://openalex.org/W2042587503","https://openalex.org/W2056558085","https://openalex.org/W2084653541","https://openalex.org/W2086684904","https://openalex.org/W2091893102","https://openalex.org/W2096761902","https://openalex.org/W2115549875","https://openalex.org/W2115566547","https://openalex.org/W2116148865","https://openalex.org/W2117302185","https://openalex.org/W2119337797","https://openalex.org/W2128659236","https://openalex.org/W2134348739","https://openalex.org/W2141454789","https://openalex.org/W2145096794","https://openalex.org/W2151693816","https://openalex.org/W2171971725","https://openalex.org/W2218353147","https://openalex.org/W2245933589","https://openalex.org/W2256307465","https://openalex.org/W2289917018","https://openalex.org/W2296052754","https://openalex.org/W2296616510","https://openalex.org/W2480981092","https://openalex.org/W2510711337","https://openalex.org/W2556237558","https://openalex.org/W2897405630","https://openalex.org/W2962904605","https://openalex.org/W2963862882","https://openalex.org/W2964340701","https://openalex.org/W3098045837","https://openalex.org/W3147515309","https://openalex.org/W3149667697","https://openalex.org/W4292079189","https://openalex.org/W4292166688"],"related_works":["https://openalex.org/W2949399405","https://openalex.org/W4301619540","https://openalex.org/W4297570801","https://openalex.org/W1639246335","https://openalex.org/W1595179898","https://openalex.org/W116214155","https://openalex.org/W1959156040","https://openalex.org/W1604839721","https://openalex.org/W2595740183","https://openalex.org/W1991950500"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,51,56,78,155],"theoretical":[3],"analysis":[4,148],"of":[5,17,46,50,58,146,157,168],"the":[6,14,30,47,112,129,133,150,158,163],"<sans-serif>CORSING</sans-serif>":[7],"(":[8],"<sans-serif>COmpRessed":[9],"SolvING</sans-serif>":[10],")":[11],"method":[12],"for":[13],"numerical":[15],"approximation":[16,45],"partial":[18],"differential":[19],"equations":[20],"based":[21],"on":[22],"compressed":[23,169],"sensing.":[24,170],"In":[25],"particular,":[26],"we":[27],"show":[28],"that":[29],"best":[31],"<inline-formula":[32,59,82,114],"content-type=\"math/mathml\">":[33,60,83,115],"<mml:math":[34,61,84,116],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[35,62,85,117],"alttext=\"s\">":[36],"<mml:semantics>":[37,65,90,119],"<mml:mi>s</mml:mi>":[38],"<mml:annotation":[39,67,98,121],"encoding=\"application/x-tex\">s</mml:annotation>":[40],"</mml:semantics>":[41,69,102,123],"</mml:math>":[42,70,103,124],"</inline-formula>":[43,71,104,125],"-term":[44],"weak":[48],"solution":[49],"PDE":[52],"with":[53,128],"respect":[54],"to":[55],"system":[57],"alttext=\"upper":[63],"N\">":[64,89],"<mml:mi>N</mml:mi>":[66,96],"encoding=\"application/x-tex\">N</mml:annotation>":[68],"trial":[72,135],"functions,":[73],"can":[74],"be":[75],"recovered":[76],"via":[77],"Petrov-Galerkin":[79],"approach":[80],"using":[81],"alttext=\"m":[86],"much-less-than":[87],"upper":[88],"<mml:mrow>":[91],"<mml:mi>m</mml:mi>":[92],"<mml:mo>":[93],"\u226a":[94],"</mml:mo>":[95],"</mml:mrow>":[97],"encoding=\"application/x-tex\">m":[99],"\\ll":[100],"N</mml:annotation>":[101],"test":[105,137],"functions.":[106],"This":[107],"recovery":[108],"is":[109,149],"guaranteed":[110],"if":[111],"local":[113],"alttext=\"a\">":[118],"<mml:mi>a</mml:mi>":[120],"encoding=\"application/x-tex\">a</mml:annotation>":[122],"-coherence":[126],"associated":[127],"bilinear":[130],"form":[131],"and":[132,136,162],"selected":[134],"bases":[138],"fulfills":[139],"suitable":[140],"decay":[141],"properties.":[142],"The":[143],"fundamental":[144],"tool":[145],"this":[147],"restricted":[151,165],"inf-sup":[152,160],"property,":[153],"i.e.,":[154],"combination":[156],"classical":[159],"condition":[161],"well-known":[164],"isometry":[166],"property":[167]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}