{"id":"https://openalex.org/W2408367358","doi":null,"title":"Fast solver for Toeplitz bidiagonal systems of linear equations","display_name":"Fast solver for Toeplitz bidiagonal systems of linear equations","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2408367358","mag":"2408367358"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.96.5018","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.96.5018","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.annales.umcs.lublin.pl/AI/2003/09.pdf","raw_type":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5052271359","display_name":"Przemys\u0142aw Stpiczy\u0144ski","orcid":"https://orcid.org/0000-0001-8661-414X","observed_orcids":["https://orcid.org/0000-0001-8661-414X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Przemys\u0142aw Stpiczy\u0144ski","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5052271359"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"1","issue":"1","first_page":"73","last_page":"79"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9955999851226807,"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":0.9955999851226807,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.004399999976158142,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.0,"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/parallel-algorithms","display_name":"parallel algorithms","score":0.8140000104904175},{"id":"https://openalex.org/keywords/gers","display_name":"Gers","score":0.8709999918937683},{"id":"https://openalex.org/keywords/openmp","display_name":"OpenMP","score":0.9660000205039978},{"id":"https://openalex.org/keywords/linear-systems-of-equations","display_name":"systems of linear equations","score":0.656000018119812},{"id":"https://openalex.org/keywords/pentium-iii","display_name":"Pentium III","score":0.5600000023841858}],"concepts":[{"id":"https://openalex.org/C46268123","wikidata":"https://www.wikidata.org/wiki/Q214314","display_name":"Pentium","level":2,"score":0.9449382424354553},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.879180908203125},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7001177072525024},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6710759401321411},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.609191358089447},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.5620408058166504},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5367087125778198},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5340520143508911},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4790269434452057},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4757646918296814},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.4495684504508972},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36921536922454834},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29677921533584595},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.07614654302597046},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05927419662475586},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.96.5018","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.96.5018","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.annales.umcs.lublin.pl/AI/2003/09.pdf","raw_type":"text"},{"id":"pmh:oai:87.246.207.98:17280","doi":null,"is_oa":false,"landing_page_url":"http://87.246.207.98/Content/17280","pdf_url":null,"source":{"id":"https://openalex.org/S4377196335","display_name":"UMCS Library (Maria Curie-Sk\u0142odowska University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I174183983","host_organization_name":"Maria Curie-Sk\u0142odowska University","host_organization_lineage":["https://openalex.org/I174183983"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"artyku\u0142"},{"id":"mag:2408367358","doi":null,"is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/umcs/umcs1.html#Stpiczynski03a","pdf_url":null,"source":{"id":"https://openalex.org/S4210184648","display_name":"Annales Universitatis Mariae Curie-Sklodowska sectio AI \u2013 Informatica","issn_l":"1732-1360","issn":["1732-1360","2083-3628"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Annales Umcs, Informatica","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W68850893","https://openalex.org/W1498557394","https://openalex.org/W1555457515","https://openalex.org/W1556859836","https://openalex.org/W1964031104","https://openalex.org/W1971947347","https://openalex.org/W1995782589","https://openalex.org/W1998875750","https://openalex.org/W2000250112","https://openalex.org/W2025529701","https://openalex.org/W2031746578","https://openalex.org/W2059591274","https://openalex.org/W2063989830","https://openalex.org/W2072701055","https://openalex.org/W2074357351","https://openalex.org/W2088465126","https://openalex.org/W2140177813","https://openalex.org/W2506642728"],"related_works":["https://openalex.org/W2983806960","https://openalex.org/W2356358151","https://openalex.org/W2532546057","https://openalex.org/W2357933428","https://openalex.org/W1827349801","https://openalex.org/W2257570909","https://openalex.org/W1978166789","https://openalex.org/W3011535154","https://openalex.org/W2003302650","https://openalex.org/W1988115914"],"abstract_inverted_index":{"We":[0,53],"present":[1,63],"a":[2,70,102],"new":[3],"efficient":[4,85],"parallel":[5],"algorithm":[6,33,94],"for":[7],"solving":[8,25],"the":[9,22,37,64,93],"first":[10],"order":[11],"linear":[12,30],"recurrence":[13],"systems":[14,28],"with":[15,59,81],"constant":[16],"coefficients":[17],"which":[18],"is":[19,34,95],"equivalent":[20],"to":[21,97],"problem":[23],"of":[24,29,39,66,87,92],"Toeplitz":[26],"bidiagonal":[27],"equations.":[31],"The":[32,89],"formulated":[35],"in":[36],"terms":[38],"level":[40],"1":[41],"and":[42,51,61],"2":[43],"BLAS":[44],"(Basic":[45],"Linear":[46],"Algebra":[47],"Subprograms)":[48],"routines":[49],"AXPY":[50],"GER.":[52],"also":[54],"discuss":[55],"its":[56],"platform-independent":[57],"implementation":[58,86],"OpenMP":[60],"finally":[62],"results":[65],"experiments":[67],"performed":[68],"on":[69],"dual":[71],"processor":[72],"Pentium":[73],"III":[74],"computer":[75],"running":[76],"under":[77],"Linux":[78],"operating":[79],"system":[80],"Altas":[82],"as":[83],"an":[84],"BLAS.":[88],"sequential":[90,104],"version":[91],"up":[96],"2.5":[98],"times":[99],"faster":[100],"than":[101],"simple":[103],"algorithm.":[105],"1.":[106]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2016-06-24T00:00:00"}