{"id":"https://openalex.org/W2068856331","doi":"https://doi.org/10.1137/070688924","title":"Error Estimates for Polynomial Krylov Approximations to Matrix Functions","display_name":"Error Estimates for Polynomial Krylov Approximations to Matrix Functions","publication_year":2008,"publication_date":"2008-12-22","ids":{"openalex":"https://openalex.org/W2068856331","doi":"https://doi.org/10.1137/070688924","mag":"2068856331"},"language":"en","primary_location":{"id":"doi:10.1137/070688924","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070688924","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/A5038317749","display_name":"Fasma Diele","orcid":"https://orcid.org/0000-0002-4846-2795"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fasma Diele","raw_affiliation_strings":["f.diele@ba.iac.cnr.it#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"f.diele@ba.iac.cnr.it#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012849259","display_name":"Igor Moret","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Igor Moret","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022073474","display_name":"Stefania Ragni","orcid":"https://orcid.org/0000-0001-5864-8406"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefania Ragni","raw_affiliation_strings":["s.ragni@ba.iac.cnr.it#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"s.ragni@ba.iac.cnr.it#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.5581,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.94557049,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"30","issue":"4","first_page":"1546","last_page":"1565"},"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":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9986000061035156,"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":0.8029409050941467},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.655565619468689},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6446466445922852},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.6093645691871643},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6027564406394958},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5513411164283752},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4991934299468994},{"id":"https://openalex.org/keywords/matrix-function","display_name":"Matrix function","score":0.4515397846698761},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.4300253391265869},{"id":"https://openalex.org/keywords/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.42752206325531006},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.42706581950187683},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4257052540779114},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4121848940849304},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.4119020998477936},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2444656789302826},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.24363943934440613},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22612795233726501},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.16005924344062805},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.07417112588882446}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8029409050941467},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.655565619468689},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6446466445922852},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.6093645691871643},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6027564406394958},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5513411164283752},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4991934299468994},{"id":"https://openalex.org/C4263655","wikidata":"https://www.wikidata.org/wiki/Q2699958","display_name":"Matrix function","level":4,"score":0.4515397846698761},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.4300253391265869},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.42752206325531006},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.42706581950187683},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4257052540779114},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4121848940849304},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.4119020998477936},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2444656789302826},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.24363943934440613},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22612795233726501},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.16005924344062805},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07417112588882446},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/070688924","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070688924","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"},{"id":"pmh:oai:arts.units.it:11368/2278356","is_oa":false,"landing_page_url":"http://hdl.handle.net/11368/2278356","pdf_url":null,"source":{"id":"https://openalex.org/S4306400480","display_name":"ArTS Archivio della ricerca di Trieste (University of Trieste https://www.units.it/)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142444530","host_organization_name":"University of Trieste","host_organization_lineage":["https://openalex.org/I142444530"],"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"},{"id":"pmh:oai:iris.unife.it:11392/2336454","is_oa":false,"landing_page_url":"http://hdl.handle.net/11392/2336454","pdf_url":null,"source":{"id":"https://openalex.org/S4306400369","display_name":"Institutional Research Information System University of Ferrara (University of Ferrara)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I201324441","host_organization_name":"University of Ferrara","host_organization_lineage":["https://openalex.org/I201324441"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1567419358","https://openalex.org/W1966583298","https://openalex.org/W1975299137","https://openalex.org/W1984347942","https://openalex.org/W1994104690","https://openalex.org/W2010652522","https://openalex.org/W2016982898","https://openalex.org/W2024126833","https://openalex.org/W2025073139","https://openalex.org/W2025324598","https://openalex.org/W2027319740","https://openalex.org/W2028948789","https://openalex.org/W2029844436","https://openalex.org/W2057602562","https://openalex.org/W2063599529","https://openalex.org/W2090501010","https://openalex.org/W2090704787","https://openalex.org/W2092112892","https://openalex.org/W2113478610","https://openalex.org/W2125426869","https://openalex.org/W2142895119"],"related_works":["https://openalex.org/W2352294950","https://openalex.org/W3046157608","https://openalex.org/W2963080977","https://openalex.org/W2356895863","https://openalex.org/W2790314694","https://openalex.org/W2404150775","https://openalex.org/W2971978007","https://openalex.org/W2383925152","https://openalex.org/W2047443007","https://openalex.org/W3174400998"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,69],"are":[4],"interested":[5],"in":[6,37],"the":[7,12,61,67],"polynomial":[8],"Krylov":[9],"approximations":[10],"for":[11,40],"computation":[13],"of":[14,46,60,66,77],"$\\varphi(A)v$,":[15],"where":[16],"A":[17],"is":[18,29,71],"a":[19,24,30,51,57],"square":[20],"matrix,":[21],"v":[22],"represents":[23],"given":[25],"vector,":[26],"and":[27,48],"$\\varphi$":[28],"suitable":[31],"function":[32],"which":[33,55],"can":[34],"be":[35],"employed":[36],"modern":[38],"integrators":[39],"differential":[41],"problems.":[42],"Our":[43],"aim":[44],"consists":[45],"proposing":[47],"analyzing":[49],"innovative":[50],"posteriori":[52],"error":[53],"estimates":[54],"allow":[56],"good":[58],"control":[59],"approximation":[62],"procedure.":[63],"The":[64],"effectiveness":[65],"results":[68],"provide":[70],"tested":[72],"on":[73],"some":[74],"numerical":[75],"examples":[76],"interest.":[78]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
