{"id":"https://openalex.org/W2153917836","doi":"https://doi.org/10.1109/icassp.2012.6288739","title":"An estimator for the eigenvalues of the system matrix of a periodic-reference LMS algorithm","display_name":"An estimator for the eigenvalues of the system matrix of a periodic-reference LMS algorithm","publication_year":2012,"publication_date":"2012-03-01","ids":{"openalex":"https://openalex.org/W2153917836","doi":"https://doi.org/10.1109/icassp.2012.6288739","mag":"2153917836"},"language":"en","primary_location":{"id":"doi:10.1109/icassp.2012.6288739","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2012.6288739","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-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/A5030073861","display_name":"Tuomas Haarnoja","orcid":"https://orcid.org/0009-0007-2973-9246"},"institutions":[{"id":"https://openalex.org/I87653560","display_name":"VTT Technical Research Centre of Finland","ror":"https://ror.org/04b181w54","country_code":"FI","type":"nonprofit","lineage":["https://openalex.org/I4210089493","https://openalex.org/I87653560"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Tuomas Haarnoja","raw_affiliation_strings":["VTT Technical Research Center of Finland, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"VTT Technical Research Center of Finland, Finland","institution_ids":["https://openalex.org/I87653560"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034426727","display_name":"Kari Tammi","orcid":"https://orcid.org/0000-0001-9376-2386"},"institutions":[{"id":"https://openalex.org/I87653560","display_name":"VTT Technical Research Centre of Finland","ror":"https://ror.org/04b181w54","country_code":"FI","type":"nonprofit","lineage":["https://openalex.org/I4210089493","https://openalex.org/I87653560"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Kari Tammi","raw_affiliation_strings":["VTT Technical Research Center of Finland, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"VTT Technical Research Center of Finland, Finland","institution_ids":["https://openalex.org/I87653560"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048402622","display_name":"Kai Zenger","orcid":"https://orcid.org/0000-0001-6138-2135"},"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":"Kai Zenger","raw_affiliation_strings":["School of Electrical Engineering, Aalto University, Aalto, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Aalto University, Aalto, Finland","institution_ids":["https://openalex.org/I9927081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17040878,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"3777","last_page":"3780"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":1.0,"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"}},{"id":"https://openalex.org/T10860","display_name":"Speech and Audio Processing","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7531173229217529},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7503769993782043},{"id":"https://openalex.org/keywords/monodromy-matrix","display_name":"Monodromy matrix","score":0.7394411563873291},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7120241522789001},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6345919370651245},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5965226888656616},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5718432068824768},{"id":"https://openalex.org/keywords/monodromy","display_name":"Monodromy","score":0.5283563733100891},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4274086356163025},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3493122458457947},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18833652138710022},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15186572074890137},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.06409290432929993},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.049403250217437744}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7531173229217529},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7503769993782043},{"id":"https://openalex.org/C2780311589","wikidata":"https://www.wikidata.org/wiki/Q6901559","display_name":"Monodromy matrix","level":3,"score":0.7394411563873291},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7120241522789001},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6345919370651245},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5965226888656616},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5718432068824768},{"id":"https://openalex.org/C96403706","wikidata":"https://www.wikidata.org/wiki/Q543956","display_name":"Monodromy","level":2,"score":0.5283563733100891},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4274086356163025},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3493122458457947},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18833652138710022},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15186572074890137},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.06409290432929993},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.049403250217437744},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icassp.2012.6288739","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2012.6288739","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1535810436","https://openalex.org/W1983567450","https://openalex.org/W2001905757","https://openalex.org/W2024730595","https://openalex.org/W2088458290","https://openalex.org/W2133635346","https://openalex.org/W2143975507","https://openalex.org/W2149350404","https://openalex.org/W2617727454","https://openalex.org/W2726904221","https://openalex.org/W3141427594","https://openalex.org/W6632223199","https://openalex.org/W6737993025","https://openalex.org/W6740227891"],"related_works":["https://openalex.org/W2374262814","https://openalex.org/W2412051952","https://openalex.org/W1988319246","https://openalex.org/W2956219273","https://openalex.org/W4246033221","https://openalex.org/W3105214509","https://openalex.org/W1974901478","https://openalex.org/W3099920733","https://openalex.org/W4401340191","https://openalex.org/W1988842602"],"abstract_inverted_index":{"The":[0,89,114,129],"convergence":[1,105],"analysis":[2],"of":[3,24,74,85,106,125],"the":[4,21,25,51,55,68,72,75,83,86,99,103,107,122,126,137],"Least":[5],"Mean":[6],"Square":[7],"(LMS)":[8],"algorithm":[9,109],"has":[10,28],"been":[11,29],"conventionally":[12],"based":[13],"on":[14],"stochastic":[15],"signals":[16],"and":[17,63,95],"describes":[18],"thus":[19,66],"only":[20,59],"average":[22],"behavior":[23],"algorithm.":[26],"It":[27],"shown":[30],"previously":[31],"that":[32],"a":[33,41],"periodic-reference":[34],"LMS":[35,108],"system":[36,44],"can":[37,47,58],"be":[38,48,60,134],"regarded":[39],"as":[40],"linear":[42],"time-periodic":[43],"whose":[45],"stability":[46],"determined":[49],"from":[50],"monodromy":[52,56,87,127],"matrix.":[53,88,128],"Generally,":[54],"matrix":[57],"solved":[61],"numerically":[62],"does":[64],"not":[65],"reveal":[67],"actual":[69],"factors":[70],"behind":[71],"dynamics":[73],"system.":[76],"This":[77],"paper":[78],"derives":[79],"an":[80],"estimator":[81,90,115,130],"for":[82,102,136],"eigenvalues":[84,124,138],"is":[91,116,131],"easy":[92],"to":[93,121,133,140],"calculate,":[94],"it":[96,120],"also":[97],"reveals":[98],"underlying":[100],"reason":[101],"bad":[104],"in":[110],"some":[111],"special":[112],"cases.":[113],"confirmed":[117],"by":[118],"comparing":[119],"precise":[123],"found":[132],"accurate":[135],"close":[139],"unity.":[141]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
