{"id":"https://openalex.org/W2053247190","doi":"https://doi.org/10.1137/12089226x","title":"Convergence Analysis of an Extended Krylov Subspace Method for the Approximation of Operator Functions in Exponential Integrators","display_name":"Convergence Analysis of an Extended Krylov Subspace Method for the Approximation of Operator Functions in Exponential Integrators","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2053247190","doi":"https://doi.org/10.1137/12089226x","mag":"2053247190"},"language":"en","primary_location":{"id":"doi:10.1137/12089226x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/12089226x","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/A5058313922","display_name":"Tanja G\u00f6ckler","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tanja G\u00f6ckler","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5082039278","display_name":"Volker Grimm","orcid":"https://orcid.org/0000-0002-6821-5388"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Volker Grimm","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058313922"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5378,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.89423776,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"51","issue":"4","first_page":"2189","last_page":"2213"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/krylov-subspace","display_name":"Krylov subspace","score":0.865612268447876},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8644722700119019},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6153456568717957},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.610720157623291},{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"Matrix exponential","score":0.5915278196334839},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5619405508041382},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.5191261172294617},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5136913657188416},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46772754192352295},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4626743197441101},{"id":"https://openalex.org/keywords/operator-norm","display_name":"Operator norm","score":0.45196279883384705},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4422139823436737},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.43097156286239624},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.22985461354255676},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.1797924041748047},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.0946468710899353},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08092179894447327}],"concepts":[{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.865612268447876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8644722700119019},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6153456568717957},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.610720157623291},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.5915278196334839},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5619405508041382},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.5191261172294617},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5136913657188416},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46772754192352295},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4626743197441101},{"id":"https://openalex.org/C68386474","wikidata":"https://www.wikidata.org/wiki/Q980557","display_name":"Operator norm","level":3,"score":0.45196279883384705},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4422139823436737},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.43097156286239624},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.22985461354255676},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.1797924041748047},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0946468710899353},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08092179894447327},{"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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/12089226x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/12089226x","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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.49000000953674316}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W187950448","https://openalex.org/W590498058","https://openalex.org/W1492498476","https://openalex.org/W1583515859","https://openalex.org/W1606157354","https://openalex.org/W1711916224","https://openalex.org/W1966504425","https://openalex.org/W1966583298","https://openalex.org/W1973474434","https://openalex.org/W1975299137","https://openalex.org/W1982334097","https://openalex.org/W1982786226","https://openalex.org/W1984347942","https://openalex.org/W1996297482","https://openalex.org/W2012708773","https://openalex.org/W2017710275","https://openalex.org/W2021036023","https://openalex.org/W2022615414","https://openalex.org/W2024126833","https://openalex.org/W2025073139","https://openalex.org/W2028948789","https://openalex.org/W2037201748","https://openalex.org/W2044543226","https://openalex.org/W2052604766","https://openalex.org/W2069950183","https://openalex.org/W2075247318","https://openalex.org/W2078757996","https://openalex.org/W2085881863","https://openalex.org/W2092112892","https://openalex.org/W2117799929","https://openalex.org/W2134645580","https://openalex.org/W2150150879","https://openalex.org/W4211077197"],"related_works":["https://openalex.org/W2042846224","https://openalex.org/W2358905935","https://openalex.org/W2942315554","https://openalex.org/W2804461272","https://openalex.org/W2040391781","https://openalex.org/W2375237787","https://openalex.org/W3134028852","https://openalex.org/W1930195566","https://openalex.org/W4287116713","https://openalex.org/W2798077753"],"abstract_inverted_index":{"We":[0,71],"analyze":[1],"the":[2,11,23,26,30,38,41,47,55,68,75,78,83,93,96],"convergence":[3,73,90],"of":[4,13,25,29,40,57,67,74,92,95],"an":[5],"extended":[6,31],"Krylov":[7,32],"subspace":[8,33],"method":[9,76],"for":[10,46,61,77],"approximation":[12,56],"operator":[14,49,80,98],"functions":[15,59],"that":[16],"appear":[17],"in":[18,82],"exponential":[19],"integrators.":[20],"For":[21],"operators,":[22],"size":[24],"polynomial":[27],"part":[28],"is":[34,106],"restricted":[35],"according":[36],"to":[37,88],"smoothness":[39],"initial":[42],"data.":[43],"This":[44],"restriction":[45],"continuous":[48,69,79],"has":[50],"a":[51,89],"significant":[52],"influence":[53],"on":[54],"matrix":[58],"evaluated":[60],"matrices":[62],"stemming":[63],"from":[64],"space":[65],"discretizations":[66],"operator.":[70],"prove":[72],"and,":[81],"discrete":[84],"case,":[85],"this":[86],"leads":[87],"independent":[91],"norm":[94],"discretized":[97],"uniformly":[99],"over":[100],"all":[101],"possible":[102],"grids.":[103],"The":[104],"analysis":[105],"illustrated":[107],"by":[108],"numerical":[109],"experiments.":[110]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
