{"id":"https://openalex.org/W2025303603","doi":"https://doi.org/10.1137/0914018","title":"Vector-Supercomputer Experiments with the Primal Affine Linear Programming Scaling Algorithm","display_name":"Vector-Supercomputer Experiments with the Primal Affine Linear Programming Scaling Algorithm","publication_year":1993,"publication_date":"1993-03-01","ids":{"openalex":"https://openalex.org/W2025303603","doi":"https://doi.org/10.1137/0914018","mag":"2025303603"},"language":"en","primary_location":{"id":"doi:10.1137/0914018","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0914018","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/A5109805555","display_name":"K. O. Kortanek","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"K. O. Kortanek","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5109805555"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9391,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.74135338,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"2","first_page":"279","last_page":"294"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9959999918937683,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/supercomputer","display_name":"Supercomputer","score":0.8286111354827881},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5977755188941956},{"id":"https://openalex.org/keywords/fortran","display_name":"Fortran","score":0.5343358516693115},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5304980278015137},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.528701901435852},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5276927947998047},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.4786195158958435},{"id":"https://openalex.org/keywords/lu-decomposition","display_name":"LU decomposition","score":0.43724074959754944},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.4199373722076416},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4197006821632385},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.41246429085731506},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37051719427108765},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3575313687324524},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.2785342335700989},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1866525411605835},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1527715027332306},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.135860413312912},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11169907450675964}],"concepts":[{"id":"https://openalex.org/C83283714","wikidata":"https://www.wikidata.org/wiki/Q121117","display_name":"Supercomputer","level":2,"score":0.8286111354827881},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5977755188941956},{"id":"https://openalex.org/C2778241615","wikidata":"https://www.wikidata.org/wiki/Q83303","display_name":"Fortran","level":2,"score":0.5343358516693115},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5304980278015137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.528701901435852},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5276927947998047},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.4786195158958435},{"id":"https://openalex.org/C123213974","wikidata":"https://www.wikidata.org/wiki/Q833089","display_name":"LU decomposition","level":4,"score":0.43724074959754944},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.4199373722076416},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4197006821632385},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.41246429085731506},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37051719427108765},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3575313687324524},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.2785342335700989},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1866525411605835},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1527715027332306},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.135860413312912},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11169907450675964},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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:10.1137/0914018","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0914018","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":37,"referenced_works":["https://openalex.org/W35240903","https://openalex.org/W106541271","https://openalex.org/W192807422","https://openalex.org/W1580929723","https://openalex.org/W1963658162","https://openalex.org/W1964101848","https://openalex.org/W1972870374","https://openalex.org/W1975993600","https://openalex.org/W1981885118","https://openalex.org/W1995769522","https://openalex.org/W2001695417","https://openalex.org/W2004480883","https://openalex.org/W2007797219","https://openalex.org/W2007801319","https://openalex.org/W2010636146","https://openalex.org/W2012825713","https://openalex.org/W2024036206","https://openalex.org/W2024448501","https://openalex.org/W2026021734","https://openalex.org/W2034118363","https://openalex.org/W2045682702","https://openalex.org/W2048741758","https://openalex.org/W2049432961","https://openalex.org/W2058079132","https://openalex.org/W2074563224","https://openalex.org/W2086067311","https://openalex.org/W2086920040","https://openalex.org/W2087576060","https://openalex.org/W2088671377","https://openalex.org/W2090214675","https://openalex.org/W2095033315","https://openalex.org/W2097897435","https://openalex.org/W2166904966","https://openalex.org/W2489906889","https://openalex.org/W2611147814","https://openalex.org/W2920966226","https://openalex.org/W4236734122"],"related_works":["https://openalex.org/W2369649360","https://openalex.org/W2344713096","https://openalex.org/W1608017769","https://openalex.org/W4318969829","https://openalex.org/W4281808068","https://openalex.org/W4386259950","https://openalex.org/W2002443693","https://openalex.org/W2041987899","https://openalex.org/W2358458784","https://openalex.org/W2908870006"],"abstract_inverted_index":{"The":[0,103,150,164],"vector-supercomputer":[1],"CRAY":[2],"series":[3],"has":[4,89],"provided":[5],"significant":[6,9,72],"speed":[7],"and":[8,16,65],"digits":[10],"accuracy":[11,88,117],"for":[12,83,136,169],"solving":[13],"difficult,":[14],"large-scale,":[15],"ill-conditioned":[17,137],"linear":[18,23],"programming":[19,24],"problems":[20,138,171],"with":[21],"the":[22,98,159,175],"(LP)":[25],"primal":[26],"scaling":[27,106,162],"algorithm":[28],"of":[29,74,97],"Dikin":[30],"[Soviet":[31],"Math.":[32],"Dokl.,":[33],"8":[34],"(1967),":[35],"pp.":[36],"674\u2013675].":[37],"Ranging":[38],"from":[39,53,174,179],"fully":[40],"dense":[41,113],"Chebyshev":[42],"approximation-type":[43],"matrices":[44,51],"to":[45,111,129,141],"highly":[46],"sparse,":[47],"relatively":[48],"small,":[49],"band-widths":[50],"generated":[52],"continuum":[54],"mechanics":[55],"problems,":[56,114],"numerical":[57],"results":[58],"are":[59,119],"presented":[60],"that":[61],"indicate":[62],"good":[63,85],"stability":[64,156],"objective":[66,86],"function":[67,87],"value":[68],"accuracy.":[69],"In":[70],"a":[71,77,93,130],"number":[73],"these":[75,112,170],"experiments,":[76],"substantial":[78],"speed-up":[79],"in":[80,144,183],"CPU":[81],"time":[82],"obtaining":[84],"been":[90],"obtained":[91],"over":[92,158],"very":[94],"stable":[95],"implementation":[96],"simplex":[99],"method,":[100],"termed":[101,125],"LINOP.":[102],"companion":[104],"QR-based":[105],"implementation,":[107,124],"SHP,":[108],"was":[109,127],"applied":[110,128],"where":[115],"high":[116],"levels":[118],"required.":[120],"A":[121],"conjugate":[122],"gradient-based":[123],"HYBY,":[126],"discretized":[131],"plane":[132],"strain":[133],"plasticity":[134],"problem":[135],"having":[139],"up":[140],"7700":[142],"equations":[143],"as":[145,147],"many":[146],"9000":[148],"variables.":[149],"FORTRAN":[151],"code":[152],"includes":[153],"an":[154],"effective":[155],"enhancement":[157],"original":[160],"affine":[161],"algorithm.":[163],"sparse":[165],"LP":[166],"matrix":[167],"generator":[168],"is":[172],"available":[173],"author":[176],"(kort@icaen.uiowa.edu)":[177],"or":[178],"Professor":[180],"E.":[181],"Christiansen":[182],"Odense,":[184],"Denmark":[185],"(edc@imada.ou.dk).":[186]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
