{"id":"https://openalex.org/W1975299137","doi":"https://doi.org/10.1137/050633846","title":"A Restarted Krylov Subspace Method for the Evaluation of Matrix Functions","display_name":"A Restarted Krylov Subspace Method for the Evaluation of Matrix Functions","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1975299137","doi":"https://doi.org/10.1137/050633846","mag":"1975299137"},"language":"en","primary_location":{"id":"doi:10.1137/050633846","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050633846","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/A5016985109","display_name":"Michael Eiermann","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Michael Eiermann","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5084624008","display_name":"Oliver G. Ernst","orcid":"https://orcid.org/0000-0002-0176-7321"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Oliver G. Ernst","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5016985109"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.7629,"has_fulltext":false,"cited_by_count":148,"citation_normalized_percentile":{"value":0.98244528,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"44","issue":"6","first_page":"2481","last_page":"2504"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9914000034332275,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.9028197526931763},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7670029401779175},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.6558084487915039},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5995625257492065},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5845069885253906},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5681661367416382},{"id":"https://openalex.org/keywords/matrix-function","display_name":"Matrix function","score":0.5631909966468811},{"id":"https://openalex.org/keywords/reciprocal","display_name":"Reciprocal","score":0.5380845069885254},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4549403488636017},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.43554651737213135},{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"Matrix exponential","score":0.4201836585998535},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4110991060733795},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3918667435646057},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21378454566001892},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.13909360766410828},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.12361633777618408},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.10329234600067139}],"concepts":[{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.9028197526931763},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7670029401779175},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.6558084487915039},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5995625257492065},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5845069885253906},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5681661367416382},{"id":"https://openalex.org/C4263655","wikidata":"https://www.wikidata.org/wiki/Q2699958","display_name":"Matrix function","level":4,"score":0.5631909966468811},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.5380845069885254},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4549403488636017},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.43554651737213135},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.4201836585998535},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4110991060733795},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3918667435646057},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21378454566001892},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.13909360766410828},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.12361633777618408},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.10329234600067139},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/050633846","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050633846","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.377.203","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.377.203","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathe.tu-freiberg.de/~ernst/PubArchive/krylovExp.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.377.3616","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.377.3616","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathe.tu-freiberg.de/~ernst/PubArchive/krylovExpRev.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.69.1216","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.69.1216","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathe.tu-freiberg.de/~ernst/PubArchive/eiermannErnstKrylovExp.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W185370267","https://openalex.org/W1575791353","https://openalex.org/W1964310563","https://openalex.org/W1984347942","https://openalex.org/W1990351032","https://openalex.org/W1993531511","https://openalex.org/W1994104690","https://openalex.org/W1998366068","https://openalex.org/W2001170250","https://openalex.org/W2007967040","https://openalex.org/W2016982898","https://openalex.org/W2020804487","https://openalex.org/W2024126833","https://openalex.org/W2029844436","https://openalex.org/W2044543226","https://openalex.org/W2057602562","https://openalex.org/W2059586807","https://openalex.org/W2060769027","https://openalex.org/W2069262775","https://openalex.org/W2073955633","https://openalex.org/W2082465767","https://openalex.org/W2085066401","https://openalex.org/W2091835635","https://openalex.org/W2092886819","https://openalex.org/W2100965560","https://openalex.org/W2104756076","https://openalex.org/W2106565812","https://openalex.org/W2128978199","https://openalex.org/W2135275160","https://openalex.org/W2139875628","https://openalex.org/W2140153041","https://openalex.org/W2170486042","https://openalex.org/W2316418224","https://openalex.org/W3037830703","https://openalex.org/W3046534683"],"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/W2798077753","https://openalex.org/W2117799929","https://openalex.org/W2529950123","https://openalex.org/W2800691151","https://openalex.org/W2018931076"],"abstract_inverted_index":{"We":[0,50],"show":[1,52],"how":[2],"the":[3,44,47,54,58,71],"Arnoldi":[4],"algorithm":[5,37,56],"for":[6,28,43,66],"approximating":[7],"a":[8,11,14,20],"function":[9],"of":[10,32,62,73],"matrix":[12],"times":[13],"vector":[15],"can":[16],"be":[17],"restarted":[18,24,36,55],"in":[19],"manner":[21],"analogous":[22],"to":[23,39],"Krylov":[25],"subspace":[26],"methods":[27],"solving":[29],"linear":[30],"systems":[31],"equations.":[33],"The":[34],"resulting":[35],"reduces":[38],"other":[40],"known":[41],"algorithms":[42],"reciprocal":[45],"and":[46,69],"exponential":[48],"functions.":[49],"further":[51],"that":[53],"inherits":[57],"superlinear":[59],"convergence":[60],"property":[61],"its":[63],"unrestarted":[64],"counterpart":[65],"entire":[67],"functions":[68],"present":[70],"results":[72],"numerical":[74],"experiments.":[75]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
