{"id":"https://openalex.org/W2018687656","doi":"https://doi.org/10.1137/140964655","title":"Uniform Approximation of $\\varphi$-Functions in Exponential Integrators by a Rational Krylov Subspace Method with Simple Poles","display_name":"Uniform Approximation of $\\varphi$-Functions in Exponential Integrators by a Rational Krylov Subspace Method with Simple Poles","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2018687656","doi":"https://doi.org/10.1137/140964655","mag":"2018687656"},"language":"en","primary_location":{"id":"doi:10.1137/140964655","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140964655","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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":4.89,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.95061728,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"35","issue":"4","first_page":"1467","last_page":"1489"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":1.0,"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":1.0,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.998199999332428,"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":0.9223685264587402},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8690778613090515},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.7261548638343811},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.7204435467720032},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.5485813617706299},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5145968198776245},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.505516529083252},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4820762276649475},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47019538283348083},{"id":"https://openalex.org/keywords/exponential-integrator","display_name":"Exponential integrator","score":0.43911847472190857},{"id":"https://openalex.org/keywords/resolvent","display_name":"Resolvent","score":0.4292592704296112},{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"Matrix exponential","score":0.429007887840271},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.42138391733169556},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.41569918394088745},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4076479375362396},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.3381977081298828},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2860611379146576}],"concepts":[{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.9223685264587402},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8690778613090515},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.7261548638343811},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.7204435467720032},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5485813617706299},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5145968198776245},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.505516529083252},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4820762276649475},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47019538283348083},{"id":"https://openalex.org/C122700484","wikidata":"https://www.wikidata.org/wiki/Q16148845","display_name":"Exponential integrator","level":5,"score":0.43911847472190857},{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.4292592704296112},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.429007887840271},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.42138391733169556},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.41569918394088745},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4076479375362396},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.3381977081298828},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2860611379146576},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140964655","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140964655","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1966583298","https://openalex.org/W1972012881","https://openalex.org/W1973474434","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/W2022615414","https://openalex.org/W2024126833","https://openalex.org/W2025073139","https://openalex.org/W2028212620","https://openalex.org/W2028948789","https://openalex.org/W2037201748","https://openalex.org/W2052604766","https://openalex.org/W2053247190","https://openalex.org/W2054535878","https://openalex.org/W2069950183","https://openalex.org/W2075247318","https://openalex.org/W2078440628","https://openalex.org/W2078757996","https://openalex.org/W2085881863","https://openalex.org/W2092112892","https://openalex.org/W2107091253","https://openalex.org/W2117799929","https://openalex.org/W4211077197"],"related_works":["https://openalex.org/W2042846224","https://openalex.org/W2942315554","https://openalex.org/W2358905935","https://openalex.org/W2127062440","https://openalex.org/W2529950123","https://openalex.org/W2798077753","https://openalex.org/W2057602562","https://openalex.org/W4327811097","https://openalex.org/W2798028937","https://openalex.org/W1984347942"],"abstract_inverted_index":{"We":[0,81,124],"consider":[1,58],"the":[2,5,22,25,34,53,59,74,93,118,126,129],"approximation":[3,60,97],"of":[4,16,24,70,108,117,128],"matrix":[6],"$\\varphi$-functions":[7],"that":[8,85,139],"appear":[9],"in":[10,33,52],"exponential":[11],"integrators":[12],"for":[13,46,92,113],"stiff":[14,20],"systems":[15],"differential":[17],"equations.":[18],"For":[19],"systems,":[21],"field-of-values":[23,51],"occurring":[26],"matrices":[27,48],"is":[28],"large":[29],"and":[30,135],"lies":[31],"somewhere":[32],"left":[35,54],"complex":[36,55],"half-plane.":[37],"In":[38],"order":[39,71,109],"to":[40],"obtain":[41],"an":[42],"efficient":[43],"method":[44,66,134],"uniformly":[45],"all":[47],"with":[49,67],"a":[50,62,87,99,114],"half-plane,":[56],"we":[57],"by":[61],"rational":[63,120,131],"Krylov":[64,95,121,132],"subspace":[65,96,122,133],"equidistant":[68],"poles":[69],"one":[72,110],"on":[73],"line":[75],"$\\mbox{Re}\\,z":[76],"=":[77],"\\gamma":[78],">":[79,105],"0$.":[80,106],"present":[82,136],"error":[83],"bounds":[84],"predict":[86],"faster":[88],"convergence":[89,127],"rate":[90],"as":[91],"resolvent":[94],"using":[98],"single":[100],"repeated":[101],"pole":[102],"at":[103],"$\\gamma":[104],"Poles":[107],"allow":[111],"moreover":[112],"parallel":[115],"implementation":[116],"corresponding":[119],"decomposition.":[123],"analyze":[125],"proposed":[130],"numerical":[137],"experiments":[138],"illustrate":[140],"our":[141],"results.":[142]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-07T14:57:38.498316","created_date":"2025-10-10T00:00:00"}
