{"id":"https://openalex.org/W1972637062","doi":"https://doi.org/10.1137/0914078","title":"A Parallel Algorithm for Reducing Symmetric Banded Matrices to Tridiagonal Form","display_name":"A Parallel Algorithm for Reducing Symmetric Banded Matrices to Tridiagonal Form","publication_year":1993,"publication_date":"1993-11-01","ids":{"openalex":"https://openalex.org/W1972637062","doi":"https://doi.org/10.1137/0914078","mag":"1972637062"},"language":"en","primary_location":{"id":"doi:10.1137/0914078","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0914078","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5070913387","display_name":"Bruno Lang","orcid":"https://orcid.org/0000-0001-9197-4836"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bruno Lang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5070913387"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1199,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.80447414,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"14","issue":"6","first_page":"1320","last_page":"1338"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9998000264167786,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9988999962806702,"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/T13126","display_name":"Scientific Research and Discoveries","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.9414463043212891},{"id":"https://openalex.org/keywords/mimd","display_name":"MIMD","score":0.8876280784606934},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.727647066116333},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.7260342240333557},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.724830687046051},{"id":"https://openalex.org/keywords/intel-ipsc","display_name":"Intel iPSC","score":0.6603081822395325},{"id":"https://openalex.org/keywords/tridiagonal-matrix-algorithm","display_name":"Tridiagonal matrix algorithm","score":0.6408612728118896},{"id":"https://openalex.org/keywords/parallel-algorithm","display_name":"Parallel algorithm","score":0.5181147456169128},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4892113208770752},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4795770049095154},{"id":"https://openalex.org/keywords/distributed-memory","display_name":"Distributed memory","score":0.4698668420314789},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4542239010334015},{"id":"https://openalex.org/keywords/shared-memory","display_name":"Shared memory","score":0.344482421875},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.11995863914489746}],"concepts":[{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.9414463043212891},{"id":"https://openalex.org/C21032095","wikidata":"https://www.wikidata.org/wiki/Q1149237","display_name":"MIMD","level":2,"score":0.8876280784606934},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.727647066116333},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.7260342240333557},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.724830687046051},{"id":"https://openalex.org/C199115840","wikidata":"https://www.wikidata.org/wiki/Q108649754","display_name":"Intel iPSC","level":3,"score":0.6603081822395325},{"id":"https://openalex.org/C176603272","wikidata":"https://www.wikidata.org/wiki/Q1819156","display_name":"Tridiagonal matrix algorithm","level":4,"score":0.6408612728118896},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.5181147456169128},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4892113208770752},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4795770049095154},{"id":"https://openalex.org/C91481028","wikidata":"https://www.wikidata.org/wiki/Q1054686","display_name":"Distributed memory","level":3,"score":0.4698668420314789},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4542239010334015},{"id":"https://openalex.org/C133875982","wikidata":"https://www.wikidata.org/wiki/Q764810","display_name":"Shared memory","level":2,"score":0.344482421875},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.11995863914489746},{"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:10.1137/0914078","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0914078","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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":12,"referenced_works":["https://openalex.org/W141418607","https://openalex.org/W1561829173","https://openalex.org/W1971901713","https://openalex.org/W1988425770","https://openalex.org/W2002257715","https://openalex.org/W2038469228","https://openalex.org/W2058221770","https://openalex.org/W2069146503","https://openalex.org/W2080986154","https://openalex.org/W2113701517","https://openalex.org/W4244968939","https://openalex.org/W4249437058"],"related_works":["https://openalex.org/W2157863322","https://openalex.org/W2360550119","https://openalex.org/W2057923237","https://openalex.org/W2094676092","https://openalex.org/W1972637062","https://openalex.org/W1991465874","https://openalex.org/W2081934892","https://openalex.org/W1582707252","https://openalex.org/W2087518631","https://openalex.org/W1987564325"],"abstract_inverted_index":{"An":[0],"algorithm":[1,16],"is":[2,17,21,53],"presented":[3],"for":[4],"reducing":[5],"symmetric":[6],"banded":[7],"matrices":[8],"to":[9,24],"tridiagonal":[10],"form":[11],"via":[12],"Householder":[13],"transformations.":[14],"The":[15],"numerically":[18],"stable":[19],"and":[20,78],"well":[22],"suited":[23],"parallel":[25],"execution":[26],"on":[27,38,55,61],"distributed":[28],"memory":[29],"multiple":[30,32,56],"instruction":[31],"data":[33],"(MIMD)":[34],"computers.":[35],"Numerical":[36],"experiments":[37],"the":[39,44,65,75],"iPSC/860":[40],"hypercube":[41],"show":[42],"that":[43],"new":[45,66],"method":[46,67],"yields":[47],"nearly":[48],"full":[49],"speedup":[50],"if":[51],"it":[52],"run":[54],"processors.":[57],"In":[58],"addition,":[59],"even":[60],"a":[62],"single":[63],"processor":[64],"usually":[68],"will":[69],"be":[70],"several":[71],"times":[72],"faster":[73],"than":[74],"corresponding":[76],"EISPACK":[77],"LAPACK":[79],"routines.":[80]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
