{"id":"https://openalex.org/W2065139587","doi":"https://doi.org/10.1137/0913050","title":"Parallel Methods for Solving Nonlinear Block Bordered Systems of Equations","display_name":"Parallel Methods for Solving Nonlinear Block Bordered Systems of Equations","publication_year":1992,"publication_date":"1992-07-01","ids":{"openalex":"https://openalex.org/W2065139587","doi":"https://doi.org/10.1137/0913050","mag":"2065139587"},"language":"en","primary_location":{"id":"doi:10.1137/0913050","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0913050","pdf_url":null,"source":{"id":"https://openalex.org/S4210181992","display_name":"SIAM Journal on Scientific and Statistical Computing","issn_l":"0196-5204","issn":["0196-5204","2168-3417"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 and Statistical 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/A5100376197","display_name":"Xiaodong Zhang","orcid":"https://orcid.org/0000-0002-1294-6069"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xiaodong Zhang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110661221","display_name":"Richard H. Byrd","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Richard H. Byrd","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5002119487","display_name":"Robert B. Schnabel","orcid":"https://orcid.org/0000-0003-1707-0294"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert B. Schnabel","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100376197"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3645,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.92936536,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"13","issue":"4","first_page":"841","last_page":"859"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.998199999332428,"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":0.998199999332428,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9940000176429749,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7699424028396606},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.7641576528549194},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5500116944313049},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.5498195290565491},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4730895161628723},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.42421025037765503},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42409494519233704},{"id":"https://openalex.org/keywords/implementation","display_name":"Implementation","score":0.4125262200832367},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3989402949810028},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33108046650886536},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12219446897506714}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7699424028396606},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.7641576528549194},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5500116944313049},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.5498195290565491},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4730895161628723},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.42421025037765503},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42409494519233704},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.4125262200832367},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3989402949810028},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33108046650886536},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12219446897506714},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/0913050","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0913050","pdf_url":null,"source":{"id":"https://openalex.org/S4210181992","display_name":"SIAM Journal on Scientific and Statistical Computing","issn_l":"0196-5204","issn":["0196-5204","2168-3417"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 and Statistical Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.48.4239","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.4239","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.wm.edu/~zhang/../hpcs/WWW/HTML/publications/papers/bbpaper.ps.Z","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.79.5631","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.79.5631","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cse.ohio-state.edu/hpcs/WWW/HTML/publications/papers/SIAM-92-paper.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1966058269","https://openalex.org/W1970105169","https://openalex.org/W1970261865","https://openalex.org/W1975563825","https://openalex.org/W1980299085","https://openalex.org/W2011039300","https://openalex.org/W2056225453","https://openalex.org/W2100828159","https://openalex.org/W2143697374","https://openalex.org/W2161563328","https://openalex.org/W2295101953","https://openalex.org/W2321653420","https://openalex.org/W2503238209","https://openalex.org/W3010287288","https://openalex.org/W3118870036","https://openalex.org/W3145363696","https://openalex.org/W4236316114","https://openalex.org/W4290044953"],"related_works":["https://openalex.org/W4286907761","https://openalex.org/W2916710807","https://openalex.org/W2413588304","https://openalex.org/W3205447645","https://openalex.org/W2009411567","https://openalex.org/W2371629703","https://openalex.org/W2097769911","https://openalex.org/W2774705104","https://openalex.org/W4250003423","https://openalex.org/W2029210135"],"abstract_inverted_index":{"A":[0],"group":[1],"of":[2,13,20,72,88,97,119,142],"parallel":[3,121],"algorithms,":[4],"and":[5,33,46,52,76,84,108],"their":[6],"implementation":[7],"for":[8,58,100],"solving":[9,59,101],"a":[10,39,129,137],"special":[11],"class":[12],"nonlinear":[14,62,104,143],"equations,":[15],"are":[16,50,80,92,106,124],"discussed.":[17],"The":[18,43,66],"type":[19],"sparsity":[21],"occurring":[22],"in":[23,28],"these":[24,98],"problems,":[25],"which":[26],"arise":[27],"VLSI":[29],"design,":[30],"structural":[31],"engineering,":[32],"many":[34],"other":[35],"areas,":[36],"is":[37,64,74],"called":[38],"block":[40,60,102,139],"bordered":[41,61,103,140],"structure.":[42],"explicit":[44],"method":[45,57,91],"several":[47],"implicit":[48,56,90,122],"methods":[49,73],"described,":[51,107],"the":[53,69,89,112,117,120],"new":[54],"corrected":[55],"problems":[63],"presented.":[65,125],"relationship":[67],"between":[68],"two":[70],"types":[71],"analyzed,":[75],"some":[77],"computational":[78],"comparisons":[79],"performed.":[81],"Several":[82],"variations":[83],"globally":[85],"convergent":[86],"modifications":[87],"also":[93],"described.":[94],"Parallel":[95],"implementations":[96],"algorithms":[99,123],"equations":[105],"experimental":[109],"results":[110],"on":[111],"Intel":[113],"hypercube":[114],"that":[115,134],"show":[116],"effectiveness":[118],"These":[126],"experiments":[127],"include":[128],"fairly":[130],"large":[131],"circuit":[132],"simulation":[133],"leads":[135],"to":[136],"multilevel":[138],"system":[141],"equations.":[144]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
