{"id":"https://openalex.org/W2047146682","doi":"https://doi.org/10.1109/78.80957","title":"Error-free solution to a Toeplitz system of equations","display_name":"Error-free solution to a Toeplitz system of equations","publication_year":1991,"publication_date":"1991-05-01","ids":{"openalex":"https://openalex.org/W2047146682","doi":"https://doi.org/10.1109/78.80957","mag":"2047146682"},"language":"en","primary_location":{"id":"doi:10.1109/78.80957","is_oa":false,"landing_page_url":"https://doi.org/10.1109/78.80957","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","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/A5053399403","display_name":"B.K. Harms","orcid":null},"institutions":[{"id":"https://openalex.org/I189590672","display_name":"Kansas State University","ror":"https://ror.org/05p1j8758","country_code":"US","type":"education","lineage":["https://openalex.org/I189590672"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. Harms","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Kansas State University, Manhattan, KS, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Kansas State University, Manhattan, KS, USA","institution_ids":["https://openalex.org/I189590672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011955599","display_name":"Sallie Keller\u2010McNulty","orcid":"https://orcid.org/0000-0001-7303-7267"},"institutions":[{"id":"https://openalex.org/I189590672","display_name":"Kansas State University","ror":"https://ror.org/05p1j8758","country_code":"US","type":"education","lineage":["https://openalex.org/I189590672"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Keller-McNulty","raw_affiliation_strings":["Department of Statistics, Kansas State University, Manhattan, KS, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Kansas State University, Manhattan, KS, USA","institution_ids":["https://openalex.org/I189590672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I189590672"],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":0.4945,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.62492869,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"39","issue":"5","first_page":"1212","last_page":"1215"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods 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/T11697","display_name":"Numerical Methods 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/T11435","display_name":"Polynomial and algebraic computation","score":0.9994999766349792,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9977999925613403,"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":0.8156188726425171},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5353617668151855},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5268539190292358},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4887983500957489},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47229936718940735},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.415127158164978},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.41467130184173584},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41377437114715576},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3356085419654846},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12422740459442139},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10992392897605896}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.8156188726425171},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5353617668151855},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5268539190292358},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4887983500957489},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47229936718940735},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.415127158164978},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.41467130184173584},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41377437114715576},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3356085419654846},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12422740459442139},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10992392897605896},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/78.80957","is_oa":false,"landing_page_url":"https://doi.org/10.1109/78.80957","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W934457470","https://openalex.org/W1502286077","https://openalex.org/W1894574293","https://openalex.org/W1976266534","https://openalex.org/W2001938560","https://openalex.org/W2004450282","https://openalex.org/W2017987659","https://openalex.org/W2063392015","https://openalex.org/W2117039934","https://openalex.org/W2153028802"],"related_works":["https://openalex.org/W2389462125","https://openalex.org/W2091997962","https://openalex.org/W151496359","https://openalex.org/W4220662591","https://openalex.org/W856465872","https://openalex.org/W1969863203","https://openalex.org/W1987843132","https://openalex.org/W1480644286","https://openalex.org/W2359223678","https://openalex.org/W2021817704"],"abstract_inverted_index":{"A":[0],"numerical":[1],"method":[2,19,65,82],"which":[3],"allows":[4],"error-free":[5,64,97],"computation":[6],"of":[7,14,24,47,96],"the":[8,22,48,90,94],"solution":[9,98],"to":[10,43,52,93],"a":[11,44,67],"Toeplitz":[12],"system":[13,23],"equations":[15,25],"is":[16,33,41],"developed.":[17],"The":[18,63,80],"requires":[20],"that":[21,32],"have":[26],"rational":[27],"entries.":[28],"To":[29],"avoid":[30],"error":[31],"inherent":[34],"in":[35],"floating-point":[36],"arithmetic,":[37],"multiple-modulus":[38],"residue":[39],"arithmetic":[40],"applied":[42],"modified":[45],"version":[46],"Levinson":[49],"algorithm":[50,54],"and":[51,59,71,78],"an":[53,87],"presented":[55,83],"by":[56],"S.Y.":[57],"Kung":[58],"Y.H.":[60],"Hu":[61],"(1983).":[62],"has":[66],"highly":[68],"parallel":[69],"structure":[70],"can":[72],"be":[73],"implemented":[74],"with":[75],"existing":[76],"software":[77],"hardware.":[79],"exact":[81],"here":[84],"serves":[85],"as":[86],"outline":[88],"for":[89],"general":[91],"approach":[92],"development":[95],"methods.>":[99]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}