{"id":"https://openalex.org/W1981602517","doi":"https://doi.org/10.1137/s0895479801383166","title":"Real-Valued, Low Rank, Circulant Approximation","display_name":"Real-Valued, Low Rank, Circulant Approximation","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1981602517","doi":"https://doi.org/10.1137/s0895479801383166","mag":"1981602517"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479801383166","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479801383166","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/A5029654954","display_name":"Moody T. Chu","orcid":"https://orcid.org/0000-0001-8544-3588"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Moody T. Chu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5076353369","display_name":"Robert J. Plemmons","orcid":"https://orcid.org/0000-0003-4021-6925"},"institutions":[{"id":"https://openalex.org/I47251452","display_name":"Wake Forest University","ror":"https://ror.org/0207ad724","country_code":"US","type":"education","lineage":["https://openalex.org/I47251452"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert J. Plemmons","raw_affiliation_strings":["Wake Forest University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wake Forest University","institution_ids":["https://openalex.org/I47251452"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.108215,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"24","issue":"3","first_page":"645","last_page":"659"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9984999895095825,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9984999895095825,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9962999820709229,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/circulant-matrix","display_name":"Circulant matrix","score":0.8345921039581299},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7104160785675049},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.6210768818855286},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5926396250724792},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5887281894683838},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.5801982879638672},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5454379916191101},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4373219609260559},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36625543236732483},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36438143253326416},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3012771010398865},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19472768902778625}],"concepts":[{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.8345921039581299},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7104160785675049},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.6210768818855286},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5926396250724792},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5887281894683838},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.5801982879638672},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5454379916191101},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4373219609260559},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36625543236732483},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36438143253326416},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3012771010398865},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19472768902778625},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895479801383166","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479801383166","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:CiteSeerX.psu:10.1.1.71.9312","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.71.9312","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www4.ncsu.edu/~mtchu/Research/Papers/circul.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W128724856","https://openalex.org/W1594234351","https://openalex.org/W2014092582","https://openalex.org/W2017415695","https://openalex.org/W2017895259","https://openalex.org/W2045667649","https://openalex.org/W2053685193","https://openalex.org/W2065578933","https://openalex.org/W2080097309","https://openalex.org/W2134572726","https://openalex.org/W2140064412","https://openalex.org/W2152004476"],"related_works":["https://openalex.org/W2117159910","https://openalex.org/W2139378013","https://openalex.org/W2044900700","https://openalex.org/W2560470131","https://openalex.org/W2049656902","https://openalex.org/W3106318770","https://openalex.org/W3144354057","https://openalex.org/W4385556248","https://openalex.org/W3213035342","https://openalex.org/W3213049004"],"abstract_inverted_index":{"Partially":[0],"due":[1],"to":[2,78,93],"the":[3,6,18,28,49,81,105],"fact":[4],"that":[5,104],"empirical":[7],"data":[8,37],"collected":[9],"by":[10,57,101],"devices":[11],"with":[12],"finite":[13],"bandwidth":[14],"often":[15],"neither":[16],"preserves":[17],"specified":[19],"structure":[20],"nor":[21],"induces":[22],"a":[23,35,53,58,63,85,95],"certain":[24],"desired":[25],"rank,":[26,109],"retrieving":[27],"nearest":[29,106],"structured":[30],"low":[31,67,108],"rank":[32],"approximation":[33,112],"from":[34],"given":[36,54],"matrix":[38,56,61],"becomes":[39],"an":[40],"imperative":[41],"task":[42],"in":[43],"many":[44],"applications.":[45],"This":[46],"paper":[47],"investigates":[48],"case":[50],"of":[51,62,88],"approximating":[52],"target":[55],"real-valued":[59,96],"circulant":[60,111],"specified,":[64],"fixed,":[65],"and":[66,110],"rank.":[68],"A":[69],"fast":[70],"Fourier":[71],"transform":[72],"(FFT)-based":[73],"numerical":[74,102],"procedure":[75],"is":[76,99,113],"proposed":[77],"speed":[79],"up":[80],"computation.":[82],"However,":[83],"since":[84],"conjugate-even":[86],"set":[87],"eigenvalues":[89],"must":[90],"be":[91],"maintained":[92],"guarantee":[94],"matrix,":[97],"it":[98],"shown":[100],"examples":[103],"real-valued,":[107],"sometimes":[114],"surprisingly":[115],"counterintuitive.":[116]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
