{"id":"https://openalex.org/W2127782322","doi":"https://doi.org/10.1145/2049673.2049676","title":"A note on shifted Hessenberg systems and frequency response computation","display_name":"A note on shifted Hessenberg systems and frequency response computation","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2127782322","doi":"https://doi.org/10.1145/2049673.2049676","mag":"2127782322"},"language":"en","primary_location":{"id":"doi:10.1145/2049673.2049676","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2049673.2049676","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","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/A5084513956","display_name":"Christopher Beattie","orcid":"https://orcid.org/0000-0003-3302-4845"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher Beattie","raw_affiliation_strings":["Virginia Polytechnic Institute and State University, Blacksburg, VA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Virginia Polytechnic Institute and State University, Blacksburg, VA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068311458","display_name":"Zlatko Drma\u010d","orcid":"https://orcid.org/0000-0001-6845-332X"},"institutions":[{"id":"https://openalex.org/I181343428","display_name":"University of Zagreb","ror":"https://ror.org/00mv6sv71","country_code":"HR","type":"education","lineage":["https://openalex.org/I181343428"]}],"countries":["HR"],"is_corresponding":false,"raw_author_name":"Zlatko Drma\u010d","raw_affiliation_strings":["University of Zagreb, Croatia","University of Zagreb, #N#CROATIA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Zagreb, Croatia","institution_ids":["https://openalex.org/I181343428"]},{"raw_affiliation_string":"University of Zagreb, #N#CROATIA","institution_ids":["https://openalex.org/I181343428"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028332862","display_name":"Serkan Gugercin","orcid":"https://orcid.org/0000-0003-4564-5999"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Serkan Gugercin","raw_affiliation_strings":["Virginia Polytechnic Institute and State University, Blacksburg, VA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Virginia Polytechnic Institute and State University, Blacksburg, VA","institution_ids":["https://openalex.org/I859038795"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7235,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.73441211,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"38","issue":"2","first_page":"1","last_page":"16"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6795171499252319},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5861536860466003},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5750628113746643},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5682852268218994},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5278826951980591},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5057995319366455},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.46819791197776794},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.41397982835769653},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3599112629890442},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.35587435960769653},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34471678733825684},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.30170270800590515},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11247560381889343}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6795171499252319},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5861536860466003},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5750628113746643},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5682852268218994},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5278826951980591},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5057995319366455},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.46819791197776794},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.41397982835769653},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3599112629890442},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.35587435960769653},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34471678733825684},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.30170270800590515},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11247560381889343},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2049673.2049676","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2049673.2049676","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.377.47","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.377.47","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.vt.edu/people/gugercin/ttpapers/GugercinB10.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3015418680","display_name":null,"funder_award_id":"0372783-2750","funder_id":"https://openalex.org/F4320321898","funder_display_name":"Ministarstvo Obrazovanja, Znanosti i Sporta"},{"id":"https://openalex.org/G4251157267","display_name":null,"funder_award_id":"DMS 050597DMS 0513542","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G8456416601","display_name":null,"funder_award_id":"FA9550-05-1-0449","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320321898","display_name":"Ministarstvo Obrazovanja, Znanosti i Sporta","ror":"https://ror.org/0507etz14"},{"id":"https://openalex.org/F4320335828","display_name":"Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg","ror":"https://ror.org/030h7k016"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W68620928","https://openalex.org/W106515373","https://openalex.org/W219019553","https://openalex.org/W1511577986","https://openalex.org/W1607408813","https://openalex.org/W1812003359","https://openalex.org/W1964587807","https://openalex.org/W1966992674","https://openalex.org/W1986380039","https://openalex.org/W1990987128","https://openalex.org/W1991352052","https://openalex.org/W2002257715","https://openalex.org/W2012454139","https://openalex.org/W2019612162","https://openalex.org/W2020804487","https://openalex.org/W2021586807","https://openalex.org/W2036050714","https://openalex.org/W2056478390","https://openalex.org/W2061771449","https://openalex.org/W2077091631","https://openalex.org/W2078675418","https://openalex.org/W2114792685","https://openalex.org/W2123854822","https://openalex.org/W2127782322","https://openalex.org/W2164788817","https://openalex.org/W6602798159","https://openalex.org/W6630618718"],"related_works":["https://openalex.org/W2135528694","https://openalex.org/W2102789413","https://openalex.org/W2096467061","https://openalex.org/W2105070871","https://openalex.org/W2940603871","https://openalex.org/W1532287630","https://openalex.org/W2028331352","https://openalex.org/W2052500721","https://openalex.org/W2082296130","https://openalex.org/W4299508867"],"abstract_inverted_index":{"In":[0,21],"this":[1],"article,":[2],"we":[3,23],"propose":[4],"a":[5,14,58],"numerical":[6],"algorithm":[7],"for":[8],"efficient":[9],"and":[10],"robust":[11],"solution":[12],"of":[13,16,62],"sequence":[15],"shifted":[17],"Hessenberg":[18],"linear":[19],"systems.":[20],"particular,":[22],"show":[24],"how":[25],"the":[26,41,63],"frequency":[27],"response":[28],"\ud835\udca2(\u03c3)":[29],"=":[30],"d":[31],"-":[32],"C":[33],"(":[34],"A":[35],"-\u03c3":[36],"I)":[37],"-1":[38],"b":[39],"in":[40],"single":[42],"input":[43],"case":[44],"can":[45],"be":[46],"computed":[47],"more":[48],"efficiently":[49],"than":[50],"with":[51],"other":[52],"state-of-the-art":[53],"methods.":[54],"We":[55],"also":[56],"provide":[57],"backward":[59],"stability":[60],"analysis":[61],"proposed":[64],"algorithm.":[65]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
