{"id":"https://openalex.org/W4385235573","doi":"https://doi.org/10.1137/22m1518062","title":"Randomized Sketching for Krylov Approximations of Large-Scale Matrix Functions","display_name":"Randomized Sketching for Krylov Approximations of Large-Scale Matrix Functions","publication_year":2023,"publication_date":"2023-07-25","ids":{"openalex":"https://openalex.org/W4385235573","doi":"https://doi.org/10.1137/22m1518062"},"language":"en","primary_location":{"id":"doi:10.1137/22m1518062","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1518062","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":true,"oa_status":"green","oa_url":"https://research.manchester.ac.uk/en/publications/a683e79d-0003-438b-9dbc-dbfb36aeeab4","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082852246","display_name":"Stefan G\u00fcttel","orcid":"https://orcid.org/0000-0003-1494-4478"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Stefan G\u00fcttel","raw_affiliation_strings":["Department of Mathematics, University of Manchester, M13 9PL Manchester, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Manchester, M13 9PL Manchester, UK","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029761211","display_name":"Marcel Schweitzer","orcid":"https://orcid.org/0000-0002-4937-2855"},"institutions":[{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Marcel Schweitzer","raw_affiliation_strings":["School of Mathematics and Natural Sciences, Bergische Universit\u00e4t Wuppertal, 42097 Wuppertal, Germany"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Natural Sciences, Bergische Universit\u00e4t Wuppertal, 42097 Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082852246"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7694,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.91971845,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"44","issue":"3","first_page":"1073","last_page":"1095"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9983999729156494,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.7273277640342712},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7204915285110474},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5556405782699585},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.5237724184989929},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5163532495498657},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5074858069419861},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4688093960285187},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4648650288581848},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.45143893361091614},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.430213987827301},{"id":"https://openalex.org/keywords/numerical-linear-algebra","display_name":"Numerical linear algebra","score":0.42705321311950684},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.4244341254234314},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.41955435276031494},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38182467222213745},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.30403685569763184},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30258849263191223},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.254386305809021},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23443281650543213},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21443238854408264}],"concepts":[{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.7273277640342712},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7204915285110474},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5556405782699585},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.5237724184989929},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5163532495498657},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5074858069419861},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4688093960285187},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4648650288581848},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.45143893361091614},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.430213987827301},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.42705321311950684},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.4244341254234314},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.41955435276031494},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38182467222213745},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.30403685569763184},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30258849263191223},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.254386305809021},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23443281650543213},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21443238854408264},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political 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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/22m1518062","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1518062","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:pure.atira.dk:openaire/a683e79d-0003-438b-9dbc-dbfb36aeeab4","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/a683e79d-0003-438b-9dbc-dbfb36aeeab4","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"G\u00fcttel, S & Schweitzer, M 2023, 'Randomized sketching for Krylov approximations of large-scale matrix functions', SIAM Journal on Matrix Analysis and Applications, vol. 44, no. 3, pp. 945-1163. https://doi.org/10.1137/22M1518062","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:openaire/a683e79d-0003-438b-9dbc-dbfb36aeeab4","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/a683e79d-0003-438b-9dbc-dbfb36aeeab4","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"G\u00fcttel, S & Schweitzer, M 2023, 'Randomized sketching for Krylov approximations of large-scale matrix functions', SIAM Journal on Matrix Analysis and Applications, vol. 44, no. 3, pp. 945-1163. https://doi.org/10.1137/22M1518062","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4694605880","display_name":"The Alan Turing Institute 20/21 - 21/22","funder_award_id":"EP/W001381/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W101236918","https://openalex.org/W282698172","https://openalex.org/W1483804921","https://openalex.org/W1529834200","https://openalex.org/W1546325740","https://openalex.org/W1969745760","https://openalex.org/W1970524119","https://openalex.org/W1975299137","https://openalex.org/W1978219552","https://openalex.org/W1997454815","https://openalex.org/W1998366068","https://openalex.org/W2000898529","https://openalex.org/W2010196418","https://openalex.org/W2013917460","https://openalex.org/W2016982898","https://openalex.org/W2022615414","https://openalex.org/W2023413246","https://openalex.org/W2037201748","https://openalex.org/W2044815321","https://openalex.org/W2048659456","https://openalex.org/W2057602562","https://openalex.org/W2075247318","https://openalex.org/W2078440628","https://openalex.org/W2091835635","https://openalex.org/W2107599050","https://openalex.org/W2117686912","https://openalex.org/W2117799929","https://openalex.org/W2127022449","https://openalex.org/W2140153041","https://openalex.org/W2150150879","https://openalex.org/W2316564661","https://openalex.org/W2500846120","https://openalex.org/W2792702316","https://openalex.org/W2798028937","https://openalex.org/W3005345825","https://openalex.org/W3099348172","https://openalex.org/W3104590783","https://openalex.org/W3112410551","https://openalex.org/W3120043998","https://openalex.org/W3144545573","https://openalex.org/W4213311204","https://openalex.org/W4230094094"],"related_works":["https://openalex.org/W2379775470","https://openalex.org/W1993483669","https://openalex.org/W1930195566","https://openalex.org/W3134028852","https://openalex.org/W4229076095","https://openalex.org/W2060439759","https://openalex.org/W102401903","https://openalex.org/W2169195255","https://openalex.org/W1994127340","https://openalex.org/W2787172707"],"abstract_inverted_index":{"The":[0,84],"computation":[1],"of":[2,6,20,40,65,86,95,125],"f(A)b,":[3],"the":[4,26,87,107,116,123,126],"action":[5],"a":[7,11,14,36,50,102],"matrix":[8,27],"function":[9],"on":[10,75,81],"vector,":[12],"is":[13,29,90],"task":[15],"arising":[16],"in":[17],"many":[18,24],"areas":[19],"scientific":[21],"computing.":[22],"In":[23],"applications,":[25],"A":[28],"sparse":[30],"but":[31],"so":[32],"large":[33],"that":[34],"only":[35],"rather":[37],"small":[38],"number":[39],"Krylov":[41],"basis":[42],"vectors":[43],"can":[44],"be":[45],"stored.":[46],"Here":[47],"we":[48],"discuss":[49],"new":[51],"approach":[52],"to":[53,115],"overcome":[54],"this":[55],"limitation":[56],"by":[57],"randomized":[58],"sketching":[59,128],"combined":[60],"with":[61],"an":[62],"integral":[63],"representation":[64],"f(A)b.":[66],"Two":[67],"different":[68],"approximation":[69],"methods":[70],"are":[71],"introduced,":[72],"one":[73],"based":[74,80],"sketched":[76,82,108],"FOM":[77,109,118],"and":[78,111],"another":[79],"GMRES.":[83],"convergence":[85],"latter":[88],"method":[89],"analyzed":[91],"for":[92,106],"Stieltjes":[93],"functions":[94],"positive":[96],"real":[97],"matrices.":[98],"We":[99],"also":[100],"derive":[101],"closed":[103],"form":[104],"expression":[105],"approximant":[110],"bound":[112],"its":[113],"distance":[114],"full":[117],"approximant.":[119],"Numerical":[120],"experiments":[121],"demonstrate":[122],"potential":[124],"presented":[127],"approaches.":[129]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":7}],"updated_date":"2026-04-02T15:55:50.835912","created_date":"2025-10-10T00:00:00"}