{"id":"https://openalex.org/W2134645580","doi":"https://doi.org/10.1002/(sici)1099-1506(200001/02)7:1<27::aid-nla185>3.0.co;2-4","title":"Efficient computation of the exponential operator for large, sparse, symmetric matrices","display_name":"Efficient computation of the exponential operator for large, sparse, symmetric matrices","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2134645580","doi":"https://doi.org/10.1002/(sici)1099-1506(200001/02)7:1<27::aid-nla185>3.0.co;2-4","mag":"2134645580"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1099-1506(200001/02)7:1<27::aid-nla185>3.0.co;2-4","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(200001/02)7:1<27::aid-nla185>3.0.co;2-4","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with 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/A5089013612","display_name":"Luca Bergamaschi","orcid":"https://orcid.org/0000-0001-8273-9674"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Luca Bergamaschi","raw_affiliation_strings":["Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Universita\u0300 di Padova, via Belzoni 7, 35131 Padova, Italy","Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Universit\u00e0 di Padova, via Belzoni 7, 35131 Padova, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Universita\u0300 di Padova, via Belzoni 7, 35131 Padova, Italy","institution_ids":["https://openalex.org/I138689650"]},{"raw_affiliation_string":"Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Universit\u00e0 di Padova, via Belzoni 7, 35131 Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103700691","display_name":"Marco Vianello","orcid":null},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco Vianello","raw_affiliation_strings":["Dipartimento di Matematica Pura e Applicata, Universita\u0300 di Padova, via Belzoni 7, 35131 Padova, Italy","Dipartimento di Matematica Pura e Applicata Universit\u00e0 di Padova via Belzoni 7 35131 Padova, ITALY"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica Pura e Applicata, Universita\u0300 di Padova, via Belzoni 7, 35131 Padova, Italy","institution_ids":["https://openalex.org/I138689650"]},{"raw_affiliation_string":"Dipartimento di Matematica Pura e Applicata Universit\u00e0 di Padova via Belzoni 7 35131 Padova, ITALY","institution_ids":["https://openalex.org/I138689650"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089013612"],"corresponding_institution_ids":["https://openalex.org/I138689650"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":3.7494,"has_fulltext":false,"cited_by_count":65,"citation_normalized_percentile":{"value":0.93567683,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"7","issue":"1","first_page":"27","last_page":"45"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9994000196456909,"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":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.784197211265564},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.7178499698638916},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6147326231002808},{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"Matrix exponential","score":0.6102486252784729},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.577214241027832},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5506899356842041},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.5447517037391663},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.5316793322563171},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5208483338356018},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4905235171318054},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4829534888267517},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.48072579503059387},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.44725775718688965},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4219537377357483},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.33326372504234314},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28708380460739136}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.784197211265564},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.7178499698638916},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6147326231002808},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.6102486252784729},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.577214241027832},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5506899356842041},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5447517037391663},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.5316793322563171},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5208483338356018},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4905235171318054},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4829534888267517},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.48072579503059387},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.44725775718688965},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4219537377357483},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.33326372504234314},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28708380460739136},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","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},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/(sici)1099-1506(200001/02)7:1<27::aid-nla185>3.0.co;2-4","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(200001/02)7:1<27::aid-nla185>3.0.co;2-4","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.117.7342","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.7342","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.unipd.it/~marcov/pdf/expo_nlaa.pdf","raw_type":"text"},{"id":"pmh:oai:www.research.unipd.it:11577/2481486","is_oa":false,"landing_page_url":"http://hdl.handle.net/11577/2481486","pdf_url":null,"source":{"id":"https://openalex.org/S4377196283","display_name":"Research Padua  Archive (University of Padua)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W6842531","https://openalex.org/W1977911260","https://openalex.org/W1984347942","https://openalex.org/W1994104690","https://openalex.org/W2006041013","https://openalex.org/W2010652522","https://openalex.org/W2016982898","https://openalex.org/W2044543226","https://openalex.org/W2047450102","https://openalex.org/W2048373502","https://openalex.org/W2057602562","https://openalex.org/W2060769027","https://openalex.org/W2068404638","https://openalex.org/W2082463306","https://openalex.org/W2095817904","https://openalex.org/W2104756076","https://openalex.org/W2109028745","https://openalex.org/W2120062331","https://openalex.org/W2130727150","https://openalex.org/W2586678101","https://openalex.org/W2798909945","https://openalex.org/W4232623018","https://openalex.org/W4243657877","https://openalex.org/W6775794996"],"related_works":["https://openalex.org/W2057602562","https://openalex.org/W2529950123","https://openalex.org/W2382532955","https://openalex.org/W2106962382","https://openalex.org/W3092940210","https://openalex.org/W2728265540","https://openalex.org/W4213342932","https://openalex.org/W2056379897","https://openalex.org/W2963641400","https://openalex.org/W2074316639"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"compare":[4],"Krylov":[5,57],"subspace":[6],"methods":[7],"with":[8,28],"Chebyshev":[9,49,78],"series":[10],"expansion":[11],"for":[12,98],"approximating":[13],"the":[14,48,66,75,87],"matrix":[15],"exponential":[16],"operator":[17],"on":[18],"large,":[19],"sparse,":[20],"symmetric":[21],"matrices.":[22],"Experimental":[23],"results":[24],"upon":[25],"negative-definite":[26],"matrices":[27],"very":[29],"large":[30],"size,":[31],"arising":[32],"from":[33],"(2D":[34],"and":[35,38,93],"3D)":[36],"FE":[37],"FD":[39],"spatial":[40],"discretization":[41],"of":[42,68,77,89],"linear":[43],"parabolic":[44],"PDEs,":[45],"demonstrate":[46],"that":[47],"method":[50],"can":[51],"be":[52],"an":[53],"effective":[54],"alternative":[55],"to":[56,80],"techniques,":[58],"especially":[59],"when":[60],"memory":[61],"bounds":[62],"do":[63],"not":[64],"allow":[65],"storage":[67],"all":[69],"Ritz":[70],"vectors.":[71],"We":[72],"also":[73],"discuss":[74],"sensitivity":[76],"convergence":[79],"extreme":[81],"eigenvalue":[82],"approximation,":[83],"as":[84,86],"well":[85],"reliability":[88],"various":[90],"a":[91,94],"priori":[92],"posteriori":[95],"error":[96],"estimates":[97],"both":[99],"methods.":[100],"Copyright":[101],"\u00a9":[102],"2000":[103],"John":[104],"Wiley":[105],"&":[106],"Sons,":[107],"Ltd.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}