{"id":"https://openalex.org/W2079275676","doi":"https://doi.org/10.1090/s0025-5718-00-01252-7","title":"Adaptive wavelet methods for elliptic operator equations: Convergence rates","display_name":"Adaptive wavelet methods for elliptic operator equations: Convergence rates","publication_year":2000,"publication_date":"2000-05-23","ids":{"openalex":"https://openalex.org/W2079275676","doi":"https://doi.org/10.1090/s0025-5718-00-01252-7","mag":"2079275676"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-00-01252-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01252-7","pdf_url":"https://www.ams.org/mcom/2001-70-233/S0025-5718-00-01252-7/S0025-5718-00-01252-7.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/2001-70-233/S0025-5718-00-01252-7/S0025-5718-00-01252-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108445641","display_name":"Albert Cohen","orcid":"https://orcid.org/0000-0003-1337-4012"},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Albert Cohen","raw_affiliation_strings":["Laboratoire d\u00e2\u0080\u0099Analyse Numerique, Universite Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris cedex 05, France","Laboratoire d'Analyse Num\u00e9rique, Universit\u00e9 Pierre et Marie Curie, 4, place Jussieu, 75252 Paris, Cedex 05, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire d\u00e2\u0080\u0099Analyse Numerique, Universite Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris cedex 05, France","institution_ids":["https://openalex.org/I39804081"]},{"raw_affiliation_string":"Laboratoire d'Analyse Num\u00e9rique, Universit\u00e9 Pierre et Marie Curie, 4, place Jussieu, 75252 Paris, Cedex 05, France","institution_ids":["https://openalex.org/I39804081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106691969","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\u00c3\u00bcr Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, 52056 Aachen, Germany","Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben\u00a055, 52056 Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00c3\u00bcr Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, 52056 Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]},{"raw_affiliation_string":"Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben\u00a055, 52056 Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110385534","display_name":"Ronald DeVore","orcid":"https://orcid.org/0009-0005-1105-5925"},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ronald DeVore","raw_affiliation_strings":["Department of Mathematics, University of South Carolina, Columbia, SC 29208","Department of Mathematics,#N#University of South Carolina,#N#Columbia, SC 29208"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of South Carolina, Columbia, SC 29208","institution_ids":["https://openalex.org/I155781252"]},{"raw_affiliation_string":"Department of Mathematics,#N#University of South Carolina,#N#Columbia, SC 29208","institution_ids":["https://openalex.org/I155781252"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5108445641"],"corresponding_institution_ids":["https://openalex.org/I39804081"],"apc_list":null,"apc_paid":null,"fwci":36.0188,"has_fulltext":true,"cited_by_count":481,"citation_normalized_percentile":{"value":0.99908458,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"70","issue":"233","first_page":"27","last_page":"75"},"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":0.9986000061035156,"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":0.9986000061035156,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9965999722480774,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.7357990741729736},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.5327121615409851},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5005841255187988},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.357738196849823},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3541167378425598}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7357990741729736},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.5327121615409851},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5005841255187988},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.357738196849823},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3541167378425598}],"mesh":[],"locations_count":12,"locations":[{"id":"doi:10.1090/s0025-5718-00-01252-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01252-7","pdf_url":"https://www.ams.org/mcom/2001-70-233/S0025-5718-00-01252-7/S0025-5718-00-01252-7.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:hdl:10068/183481","is_oa":false,"landing_page_url":"http://hdl.handle.net/10068/183481","pdf_url":null,"source":{"id":"https://openalex.org/S4377196900","display_name":"OpenGrey (Institut de l'Information Scientifique et Technique)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1295345811","host_organization_name":"Institut de l'Information Scientifique et Technique","host_organization_lineage":["https://openalex.org/I1295345811"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"I - Miscellaneous"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.207.2054","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.207.2054","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2001-70-233/S0025-5718-00-01252-7/S0025-5718-00-01252-7.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.331.7921","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.7921","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.sc.edu/~devore/publications/adapt.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.34.4487","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.4487","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ann.jussieu.fr/~cohen/adaptive.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.42.3401","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.3401","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://bigcheese.math.sc.edu/~devore/publications/adaptivepde12.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.42.8376","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.8376","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.sc.edu/~imip/98papers/9815.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.46.218","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.218","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://elc2.igpm.rwth-aachen.de/pub/dahmen/cddad_12.ps.Z","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.486.1417","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.486.1417","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.sc.edu/~devore/publications/adaptivepde12.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.96.5370","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.96.5370","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2001-70-233/S0025-5718-00-01252-7/S0025-5718-00-01252-7.pdf","raw_type":"text"},{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-025685383","is_oa":false,"landing_page_url":"http://mdz-nbn-resolving.de/urn:nbn:de:bvb:12-bsb00079998-2","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"software, multimedia"},{"id":"pmh:oai:publications.rwth-aachen.de:156217","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/record/156217","pdf_url":null,"source":{"id":"https://openalex.org/S4306401362","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of computation 70(233), 27-75 (2001).","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-00-01252-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01252-7","pdf_url":"https://www.ams.org/mcom/2001-70-233/S0025-5718-00-01252-7/S0025-5718-00-01252-7.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/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2079275676.pdf","grobid_xml":"https://content.openalex.org/works/W2079275676.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W143511922","https://openalex.org/W217896555","https://openalex.org/W580460520","https://openalex.org/W654435104","https://openalex.org/W1492326914","https://openalex.org/W1495502234","https://openalex.org/W1509975853","https://openalex.org/W1524015806","https://openalex.org/W1538588718","https://openalex.org/W1539855477","https://openalex.org/W1541161000","https://openalex.org/W1567428739","https://openalex.org/W1591068227","https://openalex.org/W1987842033","https://openalex.org/W1989594010","https://openalex.org/W1989701919","https://openalex.org/W1990591838","https://openalex.org/W1994336408","https://openalex.org/W2004240954","https://openalex.org/W2011884938","https://openalex.org/W2018971188","https://openalex.org/W2034167241","https://openalex.org/W2034419697","https://openalex.org/W2037733893","https://openalex.org/W2039066931","https://openalex.org/W2039924562","https://openalex.org/W2053424134","https://openalex.org/W2058618683","https://openalex.org/W2062024414","https://openalex.org/W2072759509","https://openalex.org/W2076142036","https://openalex.org/W2082051696","https://openalex.org/W2094585768","https://openalex.org/W2102922757","https://openalex.org/W2115566547","https://openalex.org/W2148639620","https://openalex.org/W2154172459","https://openalex.org/W2488440663","https://openalex.org/W2894656633","https://openalex.org/W3132971798","https://openalex.org/W4231428347","https://openalex.org/W4232421488","https://openalex.org/W4241914827","https://openalex.org/W4242704675","https://openalex.org/W4255272544","https://openalex.org/W4285719527","https://openalex.org/W4292166829","https://openalex.org/W6608679052"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2361861616","https://openalex.org/W2263699433","https://openalex.org/W2377979023","https://openalex.org/W2218034408","https://openalex.org/W2392921965","https://openalex.org/W2358755282","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552"],"abstract_inverted_index":{"This":[0],"paper":[1,160,345],"is":[2,65,153,161,232,275,296],"concerned":[3],"with":[4,185,286],"the":[5,14,23,38,68,129,147,159,162,225,279,283,291,299,307,357,365],"construction":[6,163],"and":[7,338],"analysis":[8,342],"of":[9,17,37,44,70,91,146,151,158,164,252,282,301,335,360],"wavelet-based":[10],"adaptive":[11,166,328],"algorithms":[12,21],"for":[13,62,271,350],"numerical":[15],"solution":[16,24,149,309],"elliptic":[18,292,336,352],"equations.":[19],"These":[20],"approximate":[22,308],"<inline-formula":[25,45,74,92,108,130,173,187,235,253,313],"content-type=\"math/mathml\">":[26,46,75,93,109,131,174,188,236,254,314],"<mml:math":[27,47,76,94,110,132,175,189,237,255,315],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[28,48,77,95,111,133,176,190,238,256,316],"alttext=\"u\">":[29,78,177],"<mml:semantics>":[30,51,79,98,114,136,178,201,241,260,319],"<mml:mi>u</mml:mi>":[31,80,179],"<mml:annotation":[32,53,81,100,116,138,180,219,243,266,321],"encoding=\"application/x-tex\">u</mml:annotation>":[33,82,181],"</mml:semantics>":[34,55,83,102,118,140,182,221,245,268,323],"</mml:math>":[35,56,84,103,119,141,183,222,246,269,324],"</inline-formula>":[36,57,85,104,120,142,184,223,247,270,325],"equation":[39],"by":[40,67,86,127,234,278],"a":[41,60,230,332],"linear":[42,89,358],"combination":[43,90],"alttext=\"upper":[49,96,112,134,191,239,317],"N\">":[50,97,113,135,240,318],"<mml:mi>N</mml:mi>":[52,99,115,137,207,242,320],"encoding=\"application/x-tex\">N</mml:annotation>":[54,101,117,139,244,322],"wavelets.":[58],"Therefore,":[59],"benchmark":[61],"their":[63,287],"performance":[64],"provided":[66],"rate":[69,231],"best":[71],"approximation":[72,171,280],"to":[73,172,289,305,312,331],"an":[87,165,170],"arbitrary":[88],"wavelets":[105,284],"(so":[106],"called":[107],"-term":[121,248],"approximation),":[122],"which":[123,168,272],"would":[124],"be":[125],"obtained":[126],"keeping":[128],"largest":[143],"wavelet":[144,339,366],"coefficients":[145],"real":[148],"(which":[150],"course":[152],"unknown).":[154],"The":[155,250,327,341],"main":[156],"result":[157],"scheme":[167],"produces":[169],"error":[186],"O":[192],"left-parenthesis":[193],"upper":[194],"N":[195],"Superscript":[196],"negative":[197],"s":[198],"Baseline":[199],"right-parenthesis\">":[200],"<mml:mrow>":[202,261],"<mml:mi>O</mml:mi>":[203],"<mml:mo":[204,216],"stretchy=\"false\">(</mml:mo>":[205],"<mml:msup>":[206],"<mml:mrow":[208],"class=\"MJX-TeXAtom-ORD\">":[209],"<mml:mo>":[210],"\u2212":[211],"</mml:mo>":[212],"<mml:mi>s</mml:mi>":[213,262],"</mml:mrow>":[214,218,265],"</mml:msup>":[215],"stretchy=\"false\">)</mml:mo>":[217],"encoding=\"application/x-tex\">O(N^{-s})</mml:annotation>":[220],"in":[224,343],"energy":[226],"norm,":[227],"whenever":[228],"such":[229],"possible":[233],"approximation.":[249],"range":[251],"alttext=\"s":[257],"greater-than":[258],"0\">":[259],"<mml:mo>&gt;</mml:mo>":[263],"<mml:mn>0</mml:mn>":[264],"encoding=\"application/x-tex\">s&gt;0</mml:annotation>":[267],"this":[273,344],"holds":[274],"only":[276],"limited":[277],"properties":[281],"together":[285],"ability":[288],"compress":[290],"operator.":[293],"Moreover,":[294],"it":[295],"shown":[297],"that":[298,362],"number":[300],"arithmetic":[302],"operations":[303],"needed":[304],"compute":[306],"stays":[310],"proportional":[311],".":[326],"algorithm":[329],"applies":[330],"wide":[333],"class":[334],"problems":[337,353],"bases.":[340],"puts":[346],"forward":[347],"new":[348],"techniques":[349],"treating":[351],"as":[354,356],"well":[355],"systems":[359],"equations":[361],"arise":[363],"from":[364],"discretization.":[367]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":46},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":20},{"year":2015,"cited_by_count":21},{"year":2014,"cited_by_count":27},{"year":2013,"cited_by_count":28},{"year":2012,"cited_by_count":29}],"updated_date":"2026-04-23T09:07:50.710637","created_date":"2025-10-10T00:00:00"}
