{"id":"https://openalex.org/W2069950183","doi":"https://doi.org/10.1137/090768084","title":"Approximation of Semigroups and Related Operator Functions by Resolvent Series","display_name":"Approximation of Semigroups and Related Operator Functions by Resolvent Series","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2069950183","doi":"https://doi.org/10.1137/090768084","mag":"2069950183"},"language":"en","primary_location":{"id":"doi:10.1137/090768084","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090768084","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5082039278","display_name":"Volker Grimm","orcid":"https://orcid.org/0000-0002-6821-5388"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Volker Grimm","raw_affiliation_strings":["volker.grimm@kit.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"volker.grimm@kit.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073661737","display_name":"Martin Gugat","orcid":"https://orcid.org/0000-0002-5281-110X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martin Gugat","raw_affiliation_strings":["gugat@am.uni-erlangen.de#TAB#"],"affiliations":[{"raw_affiliation_string":"gugat@am.uni-erlangen.de#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082039278"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4573,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.8834569,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"48","issue":"5","first_page":"1826","last_page":"1845"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9943000078201294,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8946795463562012},{"id":"https://openalex.org/keywords/resolvent","display_name":"Resolvent","score":0.8306586742401123},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.6712976098060608},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.5535644292831421},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5321119427680969},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4966283440589905},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.47151243686676025},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.46863341331481934},{"id":"https://openalex.org/keywords/analytic-semigroup","display_name":"Analytic semigroup","score":0.4664439857006073},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.46200770139694214},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.4539659917354584},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4403066337108612},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3506033420562744},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3300204277038574},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3281540274620056}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8946795463562012},{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.8306586742401123},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6712976098060608},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.5535644292831421},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5321119427680969},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4966283440589905},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.47151243686676025},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.46863341331481934},{"id":"https://openalex.org/C2779751289","wikidata":"https://www.wikidata.org/wiki/Q485292","display_name":"Analytic semigroup","level":3,"score":0.4664439857006073},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.46200770139694214},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.4539659917354584},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4403066337108612},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3506033420562744},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3300204277038574},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3281540274620056},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090768084","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090768084","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4099999964237213,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W586282074","https://openalex.org/W1483804921","https://openalex.org/W1492498476","https://openalex.org/W1515416301","https://openalex.org/W1606157354","https://openalex.org/W1966504425","https://openalex.org/W1979577425","https://openalex.org/W1984347942","https://openalex.org/W2010652522","https://openalex.org/W2014593736","https://openalex.org/W2021532930","https://openalex.org/W2066931007","https://openalex.org/W2078757996","https://openalex.org/W2085589788","https://openalex.org/W2091227064","https://openalex.org/W2328839813","https://openalex.org/W3038165843","https://openalex.org/W4211077197","https://openalex.org/W4252128025"],"related_works":["https://openalex.org/W2945455047","https://openalex.org/W2062149870","https://openalex.org/W1964813471","https://openalex.org/W2975981742","https://openalex.org/W2364132950","https://openalex.org/W4288598325","https://openalex.org/W1674480361","https://openalex.org/W2844902737","https://openalex.org/W2915024987","https://openalex.org/W2040585115"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,10,27,31,50,65,91,108,138],"approximation":[3,52,89],"of":[4,9,67,73,90,119],"semigroups":[5],"$e^{\\tau":[6,34],"A}$":[7,35],"and":[8,36,76,134],"functions":[11,33,93],"$\\varphi_j(\\tau":[12,37,94],"A)$":[13,95],"that":[14,26],"appear":[15],"in":[16,40,81,96,107,137],"exponential":[17,68],"integrators":[18,121],"by":[19,58],"resolvent":[20,28],"series.":[21],"The":[22,88],"interesting":[23],"fact":[24],"is":[25,45,53,114],"series":[29],"expresses":[30],"operator":[32,92],"A)$,":[38],"respectively,":[39],"efficiently":[41],"computable":[42],"terms.":[43],"This":[44],"important":[46],"for":[47,64,116],"semigroups,":[48],"where":[49],"new":[51],"different":[54],"from":[55],"well-known":[56],"approximations":[57],"rational":[59],"functions,":[60],"as":[61,63],"well":[62],"application":[66,118],"integrators,":[69],"which":[70,77],"are":[71,78],"currently":[72],"high":[74],"interest":[75],"usually":[79],"studied":[80],"a":[82,97],"semigroup":[83,101],"setting":[84,102],"on":[85],"Banach":[86],"spaces.":[87],"general,":[98],"strongly":[99],"continuous":[100],"has":[103],"not":[104],"been":[105],"discussed":[106],"literature":[109],"so":[110],"far,":[111],"but":[112],"this":[113],"crucial":[115],"an":[117],"these":[120],"with":[122,131],"unbounded":[123],"operators":[124,127],"or":[125],"bounded":[126],"(like":[128],"discretization":[129],"matrices)":[130],"large":[132],"norm":[133],"eigenvalues":[135],"somewhere":[136],"left":[139],"half":[140],"plane.":[141]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}