{"id":"https://openalex.org/W4386279698","doi":"https://doi.org/10.1137/22m1509825","title":"Perturbation Theory of Transfer Function Matrices","display_name":"Perturbation Theory of Transfer Function Matrices","publication_year":2023,"publication_date":"2023-08-30","ids":{"openalex":"https://openalex.org/W4386279698","doi":"https://doi.org/10.1137/22m1509825"},"language":"en","primary_location":{"id":"doi:10.1137/22m1509825","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1509825","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.aalto.fi/en/publications/f64cca4a-0600-466b-b8da-2705eaca1b94","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064797994","display_name":"Vanni Noferini","orcid":"https://orcid.org/0000-0002-1775-041X"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Vanni Noferini","raw_affiliation_strings":["Department of Mathematics and Systems Analysis, Aalto University, FI-00076, Aalto, Finland"],"raw_orcid":"https://orcid.org/0000-0002-1775-041X","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Systems Analysis, Aalto University, FI-00076, Aalto, Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057676963","display_name":"Lauri Nyman","orcid":"https://orcid.org/0009-0002-9558-0951"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Lauri Nyman","raw_affiliation_strings":["Department of Mathematics and Systems Analysis, Aalto University, FI-00076, Aalto, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Systems Analysis, Aalto University, FI-00076, Aalto, Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068751503","display_name":"Javier J. P\u00e9rez","orcid":"https://orcid.org/0000-0002-7628-6610"},"institutions":[{"id":"https://openalex.org/I6750721","display_name":"University of Montana","ror":"https://ror.org/0078xmk34","country_code":"US","type":"education","lineage":["https://openalex.org/I6750721"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Javier P\u00e9rez","raw_affiliation_strings":["Department of Mathematical Science, University of Montana, Missoula, MT 59812 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Science, University of Montana, Missoula, MT 59812 USA","institution_ids":["https://openalex.org/I6750721"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024301920","display_name":"Mar\u00eda C. Quintana","orcid":"https://orcid.org/0000-0003-3655-8690"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Mar\u00eda C. Quintana","raw_affiliation_strings":["Corresponding author. Department of Mathematics and Systems Analysis, Aalto University, PO Box 11100, FI-00076, Aalto, Finland"],"raw_orcid":"https://orcid.org/0000-0003-3655-8690","affiliations":[{"raw_affiliation_string":"Corresponding author. Department of Mathematics and Systems Analysis, Aalto University, PO Box 11100, FI-00076, Aalto, Finland","institution_ids":["https://openalex.org/I9927081"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5064797994"],"corresponding_institution_ids":["https://openalex.org/I9927081"],"apc_list":null,"apc_paid":null,"fwci":0.388,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.64929634,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"44","issue":"3","first_page":"1299","last_page":"1320"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9955999851226807,"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/mathematics","display_name":"Mathematics","score":0.8389629125595093},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7758079171180725},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.7124603986740112},{"id":"https://openalex.org/keywords/companion-matrix","display_name":"Companion matrix","score":0.6435662508010864},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.6207246780395508},{"id":"https://openalex.org/keywords/characteristic-polynomial","display_name":"Characteristic polynomial","score":0.5986548066139221},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.5703951120376587},{"id":"https://openalex.org/keywords/pole\u2013zero-plot","display_name":"Pole\u2013zero plot","score":0.5277044177055359},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5109054446220398},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.49832582473754883},{"id":"https://openalex.org/keywords/transfer-function","display_name":"Transfer function","score":0.4877077043056488},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.48473474383354187},{"id":"https://openalex.org/keywords/matrix-analysis","display_name":"Matrix analysis","score":0.47668027877807617},{"id":"https://openalex.org/keywords/matrix-function","display_name":"Matrix function","score":0.471889853477478},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.45438942313194275},{"id":"https://openalex.org/keywords/closed-loop-pole","display_name":"Closed-loop pole","score":0.45290619134902954},{"id":"https://openalex.org/keywords/transfer-matrix","display_name":"Transfer matrix","score":0.4215048551559448},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4183991551399231},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38650834560394287},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.384941041469574},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3843257427215576},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28947174549102783},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07402673363685608},{"id":"https://openalex.org/keywords/full-state-feedback","display_name":"Full state feedback","score":0.07151296734809875}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8389629125595093},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7758079171180725},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.7124603986740112},{"id":"https://openalex.org/C141495983","wikidata":"https://www.wikidata.org/wiki/Q814361","display_name":"Companion matrix","level":5,"score":0.6435662508010864},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.6207246780395508},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.5986548066139221},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5703951120376587},{"id":"https://openalex.org/C43656286","wikidata":"https://www.wikidata.org/wiki/Q2100961","display_name":"Pole\u2013zero plot","level":3,"score":0.5277044177055359},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5109054446220398},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49832582473754883},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.4877077043056488},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.48473474383354187},{"id":"https://openalex.org/C149488123","wikidata":"https://www.wikidata.org/wiki/Q17098730","display_name":"Matrix analysis","level":3,"score":0.47668027877807617},{"id":"https://openalex.org/C4263655","wikidata":"https://www.wikidata.org/wiki/Q2699958","display_name":"Matrix function","level":4,"score":0.471889853477478},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.45438942313194275},{"id":"https://openalex.org/C118807382","wikidata":"https://www.wikidata.org/wiki/Q5135313","display_name":"Closed-loop pole","level":4,"score":0.45290619134902954},{"id":"https://openalex.org/C122890649","wikidata":"https://www.wikidata.org/wiki/Q7834016","display_name":"Transfer matrix","level":2,"score":0.4215048551559448},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4183991551399231},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38650834560394287},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.384941041469574},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3843257427215576},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28947174549102783},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07402673363685608},{"id":"https://openalex.org/C204322392","wikidata":"https://www.wikidata.org/wiki/Q925922","display_name":"Full state feedback","level":3,"score":0.07151296734809875},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/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/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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/22m1509825","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1509825","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:aaltodoc.aalto.fi:123456789/124290","is_oa":true,"landing_page_url":"https://research.aalto.fi/en/publications/f64cca4a-0600-466b-b8da-2705eaca1b94","pdf_url":null,"source":{"id":"https://openalex.org/S4306401663","display_name":"Aaltodoc (Aalto University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9927081","host_organization_name":"Aalto University","host_organization_lineage":["https://openalex.org/I9927081"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"}],"best_oa_location":{"id":"pmh:oai:aaltodoc.aalto.fi:123456789/124290","is_oa":true,"landing_page_url":"https://research.aalto.fi/en/publications/f64cca4a-0600-466b-b8da-2705eaca1b94","pdf_url":null,"source":{"id":"https://openalex.org/S4306401663","display_name":"Aaltodoc (Aalto University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9927081","host_organization_name":"Aalto University","host_organization_lineage":["https://openalex.org/I9927081"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2994322868","display_name":null,"funder_award_id":"331230","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"},{"id":"https://openalex.org/G8084098287","display_name":null,"funder_award_id":"PID2019-106362GB-I00 MCIN/AEI/10.13039/501100011033/","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320321108","display_name":"Academy of Finland","ror":"https://ror.org/05k73zm37"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1581306515","https://openalex.org/W1976429547","https://openalex.org/W2060854423","https://openalex.org/W2085849252","https://openalex.org/W2140715711","https://openalex.org/W2159901087","https://openalex.org/W2163336887","https://openalex.org/W2598027716","https://openalex.org/W2962817835","https://openalex.org/W2972503543","https://openalex.org/W3009203148","https://openalex.org/W3022909171","https://openalex.org/W3041411248","https://openalex.org/W3131496751","https://openalex.org/W3142357617","https://openalex.org/W4211098084","https://openalex.org/W4237587600","https://openalex.org/W4249936766","https://openalex.org/W4254900683","https://openalex.org/W4300657400","https://openalex.org/W4306155041"],"related_works":["https://openalex.org/W2905919007","https://openalex.org/W2575230999","https://openalex.org/W2150665371","https://openalex.org/W1985103827","https://openalex.org/W4318902856","https://openalex.org/W2335071938","https://openalex.org/W2155748625","https://openalex.org/W2360459946","https://openalex.org/W4386279698","https://openalex.org/W2030835013"],"abstract_inverted_index":{"Zeros":[0],"of":[1,11,36,54,72,87,97,101,110,115,127,134,165],"rational":[2,63,88],"transfer":[3,56,70],"function":[4,57,71],"matrices":[5,15,89],"R(\u03bb":[6,59,90,98,135],")":[7,17,136],"are":[8,104],"the":[9,69,95,108,116,124,141,171],"eigenvalues":[10,164],"associated":[12],"polynomial":[13,40,74],"system":[14,41,75],"P(\u03bb":[16,43],"under":[18],"minimality":[19],"conditions.":[20],"In":[21],"this":[22,139],"paper,":[23],"we":[24,106,119,178],"define":[25],"a":[26,31,37,49,73,80,132],"structured":[27,81,155],"condition":[28,156,161],"number":[29,157,162],"for":[30,84,163],"simple":[32,50,85],"eigenvalue":[33],"\u03bb":[34,52,128],"0":[35,53,129],"(locally)":[38],"minimal":[39],"matrix":[42,58,64,166],"),":[44,99],"which":[45],"in":[46,138,149],"turn":[47],"is":[48],"zero":[51],"its":[55],").":[60,91],"Since":[61],"any":[62],"can":[65,146,173],"be":[66,147,174],"written":[67],"as":[68],"matrix,":[76],"our":[77,154,180],"analysis":[78,181],"yields":[79],"perturbation":[82],"theory":[83],"zeros":[86,96],"To":[92],"capture":[93],"all":[94],"regardless":[100],"whether":[102],"they":[103],"poles,":[105],"consider":[107],"notion":[109],"root":[111],"vectors.":[112],"As":[113],"corollaries":[114],"main":[117],"results,":[118],"pay":[120],"particular":[121],"attention":[122],"to":[123],"special":[125],"case":[126,140],"being":[130],"not":[131],"pole":[133],"since":[137],"results":[142],"get":[143],"simpler":[144],"and":[145,168],"useful":[148],"practice.":[150],"We":[151],"also":[152],"compare":[153],"with":[158],"Tisseur's":[159],"unstructured":[160],"polynomials":[167],"show":[169],"that":[170],"latter":[172],"unboundedly":[175],"larger.":[176],"Finally,":[177],"corroborate":[179],"by":[182],"numerical":[183],"experiments.":[184]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
