{"id":"https://openalex.org/W2096249340","doi":"https://doi.org/10.1109/ipdps.2004.1303284","title":"A parallel QR factorization algorithm for solving toeplitz tridiagonal systems","display_name":"A parallel QR factorization algorithm for solving toeplitz tridiagonal systems","publication_year":2004,"publication_date":"2004-06-10","ids":{"openalex":"https://openalex.org/W2096249340","doi":"https://doi.org/10.1109/ipdps.2004.1303284","mag":"2096249340"},"language":"en","primary_location":{"id":"doi:10.1109/ipdps.2004.1303284","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ipdps.2004.1303284","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"18th International Parallel and Distributed Processing Symposium, 2004. Proceedings.","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/A5108486368","display_name":"R.E. Shaw","orcid":null},"institutions":[{"id":"https://openalex.org/I106938459","display_name":"University of New Brunswick","ror":"https://ror.org/05nkf0n29","country_code":"CA","type":"education","lineage":["https://openalex.org/I106938459"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"R.E. Shaw","raw_affiliation_strings":["Department of Computer Science & Applied Statistics, University of New Brunswick, Saint John's, NB, Canada","Dept. of Comput. Sci. & Applied Stat., New Brunswick Univ., Saint John, NB, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science & Applied Statistics, University of New Brunswick, Saint John's, NB, Canada","institution_ids":["https://openalex.org/I106938459"]},{"raw_affiliation_string":"Dept. of Comput. Sci. & Applied Stat., New Brunswick Univ., Saint John, NB, Canada","institution_ids":["https://openalex.org/I106938459"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110219117","display_name":"L.E. Garey","orcid":null},"institutions":[{"id":"https://openalex.org/I106938459","display_name":"University of New Brunswick","ror":"https://ror.org/05nkf0n29","country_code":"CA","type":"education","lineage":["https://openalex.org/I106938459"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"L.E. Garey","raw_affiliation_strings":["Department of Computer Science & Applied Statistics, University of New Brunswick, Saint John's, NB, Canada","Dept. of Comput. Sci. & Applied Stat., New Brunswick Univ., Saint John, NB, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science & Applied Statistics, University of New Brunswick, Saint John's, NB, Canada","institution_ids":["https://openalex.org/I106938459"]},{"raw_affiliation_string":"Dept. of Comput. Sci. & Applied Stat., New Brunswick Univ., Saint John, NB, Canada","institution_ids":["https://openalex.org/I106938459"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070264847","display_name":"Andy White","orcid":null},"institutions":[{"id":"https://openalex.org/I106938459","display_name":"University of New Brunswick","ror":"https://ror.org/05nkf0n29","country_code":"CA","type":"education","lineage":["https://openalex.org/I106938459"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"A.M. White","raw_affiliation_strings":["Department of Computer Science & Applied Statistics, University of New Brunswick, Saint John's, NB, Canada","Dept. of Comput. Sci. & Applied Stat., New Brunswick Univ., Saint John, NB, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science & Applied Statistics, University of New Brunswick, Saint John's, NB, Canada","institution_ids":["https://openalex.org/I106938459"]},{"raw_affiliation_string":"Dept. of Comput. Sci. & Applied Stat., New Brunswick Univ., Saint John, NB, Canada","institution_ids":["https://openalex.org/I106938459"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I106938459"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16734892,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":null,"first_page":"235","last_page":"241"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.968999981880188,"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":0.968999981880188,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9017000198364258,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.8774490356445312},{"id":"https://openalex.org/keywords/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.859352707862854},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.7370700240135193},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6402603387832642},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6081418991088867},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5840505957603455},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.551357626914978},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.5046635866165161},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5035874247550964},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.49736717343330383},{"id":"https://openalex.org/keywords/parallel-algorithm","display_name":"Parallel algorithm","score":0.4847085475921631},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4588300883769989},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3037673234939575},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.11160984635353088},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.05737081170082092}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.8774490356445312},{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.859352707862854},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.7370700240135193},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6402603387832642},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6081418991088867},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5840505957603455},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.551357626914978},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.5046635866165161},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5035874247550964},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.49736717343330383},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.4847085475921631},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4588300883769989},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3037673234939575},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.11160984635353088},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.05737081170082092},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ipdps.2004.1303284","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ipdps.2004.1303284","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"18th International Parallel and Distributed Processing Symposium, 2004. Proceedings.","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":12,"referenced_works":["https://openalex.org/W3477132","https://openalex.org/W1532296632","https://openalex.org/W1958644447","https://openalex.org/W1982092007","https://openalex.org/W1986508690","https://openalex.org/W2032119889","https://openalex.org/W2132084488","https://openalex.org/W2134676649","https://openalex.org/W2155553169","https://openalex.org/W2160634196","https://openalex.org/W6640876957","https://openalex.org/W7015474855"],"related_works":["https://openalex.org/W3158390160","https://openalex.org/W4309994710","https://openalex.org/W2144962567","https://openalex.org/W2727575785","https://openalex.org/W2021639088","https://openalex.org/W2029459760","https://openalex.org/W3096021259","https://openalex.org/W2078349096","https://openalex.org/W2002598339","https://openalex.org/W2150953077"],"abstract_inverted_index":{"Summary":[0],"form":[1],"only":[2],"given.":[3],"QR":[4,51,60],"methods":[5],"for":[6],"solving":[7],"Toeplitz":[8,57],"tridiagonal":[9,58],"systems":[10,38],"are":[11],"well":[12],"developed":[13],"with":[14],"applications":[15],"in":[16,43],"numerous":[17],"interdisciplinary":[18],"fields.":[19],"There":[20],"is":[21,62],"a":[22,89],"strong":[23],"motivation":[24],"to":[25,35,40,55,79],"develop":[26],"faster,":[27],"more":[28,31],"efficient":[29],"and,":[30],"importantly,":[32],"scalable":[33],"algorithms":[34,53,72],"factor":[36],"such":[37],"due":[39],"their":[41],"significance":[42],"many":[44],"scientific":[45],"applications.":[46],"We":[47],"present":[48],"two":[49],"parallel":[50,71],"factorization":[52,61],"used":[54],"solve":[56],"systems.":[59],"accomplished":[63],"using":[64],"Householder":[65],"reflections":[66],"and":[67,76],"Givens":[68],"rotations.":[69],"These":[70],"exhibit":[73],"high":[74],"scalability":[75],"near":[77],"linear":[78],"superlinear":[80],"speedup":[81],"on":[82,88],"large":[83],"system":[84],"sizes":[85],"when":[86],"implemented":[87],"distributed":[90],"system.":[91]},"counts_by_year":[],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}