{"id":"https://openalex.org/W2056075924","doi":"https://doi.org/10.1137/s0895479899363526","title":"Principal Pivoting Method for Solving Column Sufficient Complementarity Problems","display_name":"Principal Pivoting Method for Solving Column Sufficient Complementarity Problems","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2056075924","doi":"https://doi.org/10.1137/s0895479899363526","mag":"2056075924"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479899363526","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479899363526","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5076639922","display_name":"A. L. N. Murthy","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"A. L. N. Murthy","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5113440282","display_name":"G. S. R. Murthy","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. S. R. Murthy","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076639922"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.16858655,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"22","issue":"2","first_page":"527","last_page":"532"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994000196456909,"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":0.9994000196456909,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9977999925613403,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9861999750137329,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8307552337646484},{"id":"https://openalex.org/keywords/linear-complementarity-problem","display_name":"Linear complementarity problem","score":0.7825583219528198},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.7122689485549927},{"id":"https://openalex.org/keywords/complementarity-theory","display_name":"Complementarity theory","score":0.6135712265968323},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.5669600367546082},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5178685188293457},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4892277717590332},{"id":"https://openalex.org/keywords/column","display_name":"Column (typography)","score":0.47352930903434753},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.45306429266929626},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4166450500488281},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41312289237976074},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.33501338958740234},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2742881774902344},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.2704890966415405},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08852994441986084},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08119019865989685}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8307552337646484},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.7825583219528198},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.7122689485549927},{"id":"https://openalex.org/C85404239","wikidata":"https://www.wikidata.org/wiki/Q5156417","display_name":"Complementarity theory","level":3,"score":0.6135712265968323},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.5669600367546082},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5178685188293457},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4892277717590332},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.47352930903434753},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.45306429266929626},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4166450500488281},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41312289237976074},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.33501338958740234},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2742881774902344},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2704890966415405},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08852994441986084},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08119019865989685},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479899363526","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479899363526","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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":11,"referenced_works":["https://openalex.org/W584634945","https://openalex.org/W1965218049","https://openalex.org/W1970000960","https://openalex.org/W1981752806","https://openalex.org/W2000151369","https://openalex.org/W2052236232","https://openalex.org/W2058037878","https://openalex.org/W2083236966","https://openalex.org/W2089649903","https://openalex.org/W2404023694","https://openalex.org/W4243886742"],"related_works":["https://openalex.org/W2052366866","https://openalex.org/W4220847489","https://openalex.org/W2125058146","https://openalex.org/W2016940464","https://openalex.org/W2100762546","https://openalex.org/W2358901572","https://openalex.org/W2276648117","https://openalex.org/W2028943836","https://openalex.org/W2073956072","https://openalex.org/W2030388112"],"abstract_inverted_index":{"The":[0],"linear":[1,113],"complementarity":[2,114],"problem":[3,80],"(q,":[4,69],"A)":[5,70],"is":[6,47,52,126],"to":[7,64,68,76,111,127,135],"find,":[8],"for":[9],"a":[10,20,28,53,60,66,107],"given":[11],"real":[12,21],"square":[13],"matrix":[14],"A":[15,34,51],"of":[16,25,99,106],"order":[17,26],"n":[18],"and":[19,40,75,87,102],"column":[22,141],"vector":[23,30],"q":[24,37],"n,":[27],"nonnegative":[29],"z":[31,35,42],"such":[32],"that":[33,49,78,129],"+":[36,43],"\\geq":[38],"0$":[39],"zt(A":[41],"q)":[44],"=0.":[45],"It":[46],"known":[48],"when":[50],"positive":[54],"semidefinite":[55],"matrix,":[56],"one":[57,74],"can":[58,132],"use":[59],"principal":[61,108],"pivoting":[62,109],"method":[63],"compute":[65],"solution":[67,83],"if":[71],"it":[72],"has":[73,81],"conclude":[77],"the":[79,97,104,138],"no":[82],"otherwise.":[84],"Cottle,":[85],"Pang,":[86],"Venkateswaran":[88],"[Linear":[89],"Algebra":[90],"Appl.,":[91],"114/115":[92],"(1989),":[93],"pp.":[94],"231--249]":[95],"introduced":[96],"class":[98],"sufficient":[100,118,142],"matrices":[101],"widened":[103],"scope":[105],"algorithm":[110,131],"solve":[112,136],"problems":[115,139],"with":[116,140],"row":[117],"matrices.":[119,143],"Our":[120],"main":[121],"result":[122],"in":[123],"this":[124,130],"article":[125],"show":[128],"be":[133],"extended":[134],"even":[137]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}