{"id":"https://openalex.org/W1555066457","doi":"https://doi.org/10.1109/icassp.1987.1169533","title":"Vector algorithms for computing QR and Cholesky factors of close-to-Toeplitz matrices","display_name":"Vector algorithms for computing QR and Cholesky factors of close-to-Toeplitz matrices","publication_year":2005,"publication_date":"2005-03-24","ids":{"openalex":"https://openalex.org/W1555066457","doi":"https://doi.org/10.1109/icassp.1987.1169533","mag":"1555066457"},"language":"en","primary_location":{"id":"doi:10.1109/icassp.1987.1169533","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.1987.1169533","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing","raw_type":"proceedings-article"},"type":"conference-paper","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/A5113141577","display_name":"C.J. Demeure","orcid":null},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. Demeure","raw_affiliation_strings":["Electrical and Computer Engineering, University of Colorado, Boulder, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080469112","display_name":"Louis L. Scharf","orcid":"https://orcid.org/0000-0003-1764-9335"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L. Scharf","raw_affiliation_strings":["Electrical and Computer Engineering, University of Colorado, Boulder, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I188538660"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":null,"first_page":"1851","last_page":"1854"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11130","display_name":"Coding theory and cryptography","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.9341867566108704},{"id":"https://openalex.org/keywords/cholesky-decomposition","display_name":"Cholesky decomposition","score":0.9162659645080566},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5926113128662109},{"id":"https://openalex.org/keywords/reflection","display_name":"Reflection (computer programming)","score":0.5619069933891296},{"id":"https://openalex.org/keywords/levinson-recursion","display_name":"Levinson recursion","score":0.4698452353477478},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4677303731441498},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4558606743812561},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4255688786506653},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4038079082965851},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18898612260818481},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.11628428101539612}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.9341867566108704},{"id":"https://openalex.org/C34727166","wikidata":"https://www.wikidata.org/wiki/Q515375","display_name":"Cholesky decomposition","level":3,"score":0.9162659645080566},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5926113128662109},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.5619069933891296},{"id":"https://openalex.org/C122212055","wikidata":"https://www.wikidata.org/wiki/Q11679774","display_name":"Levinson recursion","level":3,"score":0.4698452353477478},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4677303731441498},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4558606743812561},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4255688786506653},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4038079082965851},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18898612260818481},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.11628428101539612},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icassp.1987.1169533","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.1987.1169533","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing","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":5,"referenced_works":["https://openalex.org/W1830551853","https://openalex.org/W2028279303","https://openalex.org/W2050865647","https://openalex.org/W2066304584","https://openalex.org/W2150472686"],"related_works":["https://openalex.org/W2045714585","https://openalex.org/W2374553943","https://openalex.org/W1654107233","https://openalex.org/W1987843132","https://openalex.org/W2182312572","https://openalex.org/W2201692517","https://openalex.org/W1666266471","https://openalex.org/W2028279303","https://openalex.org/W1830551853","https://openalex.org/W3016581522"],"abstract_inverted_index":{"We":[0,20],"review":[1],"the":[2,7,22,38,46,53,81,94],"coupled":[3],"vector":[4,40],"recursions":[5,63,74,91],"for":[6,92],"Levinson,":[8],"Cybenko":[9,70,73],"and":[10,15,28,51,85],"LeRoux-Gueguen":[11,66,90],"algorithms":[12,23,33],"that":[13,30],"Cholesky":[14],"QR":[16],"factor":[17],"Toeplitz":[18],"matrices.":[19],"generalize":[21],"to":[24,79,88],"include":[25],"close-to-Toeplitz":[26],"matrices,":[27],"show":[29],"these":[31],"generalized":[32,61,65,69,82,89],"may":[34],"be":[35],"imbedded":[36],"in":[37],"same":[39],"recursions.":[41,71],"Then,":[42],"depending":[43],"on":[44],"how":[45,52],"initial":[47],"conditions":[48],"are":[49,56],"set,":[50],"reflection":[54,83],"coefficients":[55,84],"computed,":[57],"one":[58],"gets":[59],"either":[60],"Levinson":[62],"[1],":[64],"recursions,":[67],"or":[68],"The":[72],"produce":[75],"an":[76],"interesting":[77],"way":[78],"compute":[80],"also":[86],"lead":[87],"all":[93],"cases":[95],"of":[96],"linear":[97],"prediction.":[98]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}