{"id":"https://openalex.org/W2082784282","doi":"https://doi.org/10.1090/s0025-5718-05-01807-7","title":"Computation of differential operators in wavelet coordinates","display_name":"Computation of differential operators in wavelet coordinates","publication_year":2005,"publication_date":"2005-12-08","ids":{"openalex":"https://openalex.org/W2082784282","doi":"https://doi.org/10.1090/s0025-5718-05-01807-7","mag":"2082784282"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-05-01807-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01807-7","pdf_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-05-01807-7/S0025-5718-05-01807-7.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/2006-75-254/S0025-5718-05-01807-7/S0025-5718-05-01807-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053230806","display_name":"Gantumur Tsogtgerel","orcid":"https://orcid.org/0000-0001-8788-8505"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Tsogtgerel Gantumur","raw_affiliation_strings":["Department of Mathematics, Utrecht University, P. O. Box 80.010, NL-3508 TA Utrecht, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Utrecht University, P. O. Box 80.010, NL-3508 TA Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035602683","display_name":"Rob Stevenson","orcid":"https://orcid.org/0000-0001-7623-3060"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Rob Stevenson","raw_affiliation_strings":["Department of Mathematics, Utrecht University, P. O. Box 80.010, NL-3508 TA Utrecht, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Utrecht University, P. O. Box 80.010, NL-3508 TA Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053230806"],"corresponding_institution_ids":["https://openalex.org/I193662353"],"apc_list":null,"apc_paid":null,"fwci":3.2844,"has_fulltext":true,"cited_by_count":59,"citation_normalized_percentile":{"value":0.9276419,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"75","issue":"254","first_page":"697","last_page":"709"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9998000264167786,"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":0.9991999864578247,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.6076208353042603},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5124938488006592},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5010008811950684},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48846951127052307},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38316312432289124},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3620653748512268},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20066702365875244},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.10282683372497559}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6076208353042603},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5124938488006592},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5010008811950684},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48846951127052307},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38316312432289124},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3620653748512268},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20066702365875244},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.10282683372497559},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-05-01807-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01807-7","pdf_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-05-01807-7/S0025-5718-05-01807-7.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:oai:CiteSeerX.psu:10.1.1.130.2656","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.130.2656","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucsd.edu/~gtsogtge/docs/pubs/computdif.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.154.2492","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.2492","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/2006-75-254/S0025-5718-05-01807-7/S0025-5718-05-01807-7.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.77.8772","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.77.8772","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ruu.nl/publications/preprints/1306.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-05-01807-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01807-7","pdf_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-05-01807-7/S0025-5718-05-01807-7.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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2082784282.pdf","grobid_xml":"https://content.openalex.org/works/W2082784282.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W195078069","https://openalex.org/W1483446983","https://openalex.org/W1539855477","https://openalex.org/W1988406495","https://openalex.org/W1992513401","https://openalex.org/W2004261587","https://openalex.org/W2015219711","https://openalex.org/W2042035749","https://openalex.org/W2045050233","https://openalex.org/W2048268779","https://openalex.org/W2048834141","https://openalex.org/W2058288586","https://openalex.org/W2062728462","https://openalex.org/W2099475094","https://openalex.org/W2108933660","https://openalex.org/W4231428347","https://openalex.org/W6628966664","https://openalex.org/W6632328641"],"related_works":["https://openalex.org/W1482827353","https://openalex.org/W3096340483","https://openalex.org/W2088892953","https://openalex.org/W1606423697","https://openalex.org/W2021660296","https://openalex.org/W2137171564","https://openalex.org/W2946733187","https://openalex.org/W2154005220","https://openalex.org/W2050338537","https://openalex.org/W3116894630"],"abstract_inverted_index":{"In":[0],"[":[1,414],"<italic>Found.":[2],"Comput.":[3],"Math.</italic>":[4],",":[5,184,336,412,419,457],"2":[6],"(2002),":[7],"pp.":[8,422],"203\u2013245],":[9],"Cohen,":[10],"Dahmen,":[11],"and":[12,37,40,195,390,394],"DeVore":[13],"proposed":[14],"an":[15,60,71,85],"adaptive":[16,86,207],"wavelet":[17,46,102,200,371,385],"algorithm":[18],"for":[19,48,164,387,395],"solving":[20],"general":[21],"operator":[22,27,55],"equations.":[23],"Assuming":[24],"that":[25,41,91,426,459],"the":[26,54,78,93,96,101,189,193,196,199,206,363,370,384,396,463],"defines":[28],"a":[29,34,42,358],"boundedly":[30],"invertible":[31],"mapping":[32],"between":[33],"Hilbert":[35,50],"space":[36,51],"its":[38],"dual,":[39],"Riesz":[43],"basis":[44,103,372],"of":[45,77,95,192,198,227,360,399,462],"type":[47],"this":[49],"is":[52,57,68,82,186,466],"available,":[53],"equation":[56],"transformed":[58],"into":[59],"equivalent":[61],"well-posed":[62],"infinite":[63,79,364],"matrix-vector":[64],"system.":[65],"This":[66],"system":[67],"solved":[69],"by":[70,84,188,205,376],"iterative":[72],"method,":[73],"where":[74],"each":[75,460],"application":[76],"stiffness":[80,365,464],"matrix":[81,366,465],"replaced":[83],"approximation.":[87],"It":[88],"was":[89],"shown":[90],"if":[92],"errors":[94,226],"best":[97],"linear":[98],"combinations":[99],"from":[100],"with":[104,209,337,367],"<inline-formula":[105,120,166,210,228,278,311,338,400,427],"content-type=\"math/mathml\">":[106,121,167,211,229,279,312,339,401,428],"<mml:math":[107,122,168,212,230,280,313,340,402,429],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[108,123,169,213,231,281,314,341,403,430],"alttext=\"upper":[109,214],"N\">":[110,215],"<mml:semantics>":[111,135,173,216,243,289,320,345,405,437],"<mml:mi>N</mml:mi>":[112,146,217,254,299],"<mml:annotation":[113,158,179,218,266,303,331,352,407,451],"encoding=\"application/x-tex\">N</mml:annotation>":[114,219],"</mml:semantics>":[115,161,181,220,269,306,333,354,409,454],"</mml:math>":[116,162,182,221,270,307,334,355,410,455],"</inline-formula>":[117,163,183,222,271,308,335,356,411,456],"terms":[118,223],"are":[119],"alttext=\"script":[124,232,282],"upper":[125,128,233,236,283,286],"O":[126,234,284],"left-parenthesis":[127,235,285],"N":[129,237,287],"Superscript":[130,238,318,343,432],"negative":[131,239],"s":[132,240,317],"Baseline":[133,241,434],"right-parenthesis\">":[134,242,288],"<mml:mrow>":[136,174,244,290,321,438],"<mml:mrow":[137,147,245,255,291,441],"class=\"MJX-TeXAtom-ORD\">":[138,148,246,256,292,442],"<mml:mi":[139,247,293],"class=\"MJX-tex-caligraphic\"":[140,248,294],"mathvariant=\"script\">O</mml:mi>":[141,249,295],"</mml:mrow>":[142,153,157,178,250,261,265,296,302,330,446,450],"<mml:mo":[143,155,251,263,297,300],"stretchy=\"false\">(</mml:mo>":[144,252,298],"<mml:msup>":[145,253,324,346,439],"<mml:mo>":[149,257,326,348,443],"\u2212":[150,258],"</mml:mo>":[151,259,328,350,445],"<mml:mi>s</mml:mi>":[152,175,260,322,325,347,406,440,449],"</mml:msup>":[154,262,329,351,447],"stretchy=\"false\">)</mml:mo>":[156,264,301],"encoding=\"application/x-tex\">\\mathcal":[159,267,304],"{O}(N^{-s})</mml:annotation>":[160,268],"some":[165],"alttext=\"s":[170,315,342,431],"greater-than":[171,316,435],"0\">":[172],"<mml:mo>&gt;</mml:mo>":[176,323,448],"<mml:mn>0</mml:mn>":[177],"encoding=\"application/x-tex\">s&gt;0</mml:annotation>":[180],"which":[185],"determined":[187],"Besov":[190],"regularity":[191],"solution":[194],"order":[197],"basis,":[201,386],"then":[202],"approximations":[203],"yielded":[204],"method":[208],"also":[224],"have":[225],".":[272],"Moreover,":[273],"their":[274],"computation":[275],"takes":[276],"only":[277],"{O}(N)</mml:annotation>":[305],"operations,":[309],"<italic>provided</italic>":[310],"asterisk\">":[319,344],"\u2217":[327,349,444],"encoding=\"application/x-tex\">s&gt;s^*</mml:annotation>":[332],"encoding=\"application/x-tex\">s^*</mml:annotation>":[353],"being":[357],"measure":[359],"how":[361],"well":[362],"respect":[368],"to":[369],"can":[373],"be":[374],"approximated":[375],"computable":[377],"sparse":[378],"matrices.":[379],"Under":[380],"appropriate":[381],"conditions":[382],"on":[383],"both":[388],"differential":[389],"singular":[391],"integral":[392],"operators":[393],"relevant":[397],"range":[398],"alttext=\"s\">":[404],"encoding=\"application/x-tex\">s</mml:annotation>":[408],"in":[413],"<italic>SIAM":[415],"J.":[416],"Math.":[417],"Anal.</italic>":[418],"35(5)":[420],"(2004),":[421],"1110\u20131132]":[423],"we":[424],"showed":[425],"asterisk":[433],"s\">":[436],"encoding=\"application/x-tex\">s^{\\ast":[452],"}&gt;s</mml:annotation>":[453],"<italic>assuming</italic>":[458],"entry":[461],"exactly":[467],"available":[468],"at":[469],"unit":[470],"cost.":[471],"Ge":[472]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":33},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}