{"id":"https://openalex.org/W2091275975","doi":"https://doi.org/10.1109/cacsd.2010.5612693","title":"A numerical evaluation of highly accurate multiple-precision arithmetic version of semidefinite programming solver: SDPA-GMP, -QD and -DD.","display_name":"A numerical evaluation of highly accurate multiple-precision arithmetic version of semidefinite programming solver: SDPA-GMP, -QD and -DD.","publication_year":2010,"publication_date":"2010-09-01","ids":{"openalex":"https://openalex.org/W2091275975","doi":"https://doi.org/10.1109/cacsd.2010.5612693","mag":"2091275975"},"language":"en","primary_location":{"id":"doi:10.1109/cacsd.2010.5612693","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cacsd.2010.5612693","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Symposium on Computer-Aided Control System Design","raw_type":"proceedings-article"},"type":"conference-paper","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/A5101768061","display_name":"Maho Nakata","orcid":"https://orcid.org/0000-0002-5430-841X"},"institutions":[{"id":"https://openalex.org/I4210165842","display_name":"RIKEN Center for Advanced Photonics","ror":"https://ror.org/05vmjks78","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210165842"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Maho Nakata","raw_affiliation_strings":["Advanced Center for Computing and Communication, RIKEN, Saitama, Japan","Advanced Center for Computing and Communication, RIKEN Saitama, 351-0198 JAPAN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Advanced Center for Computing and Communication, RIKEN, Saitama, Japan","institution_ids":["https://openalex.org/I4210165842"]},{"raw_affiliation_string":"Advanced Center for Computing and Communication, RIKEN Saitama, 351-0198 JAPAN","institution_ids":["https://openalex.org/I4210165842"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101768061"],"corresponding_institution_ids":["https://openalex.org/I4210165842"],"apc_list":null,"apc_paid":null,"fwci":9.8609,"has_fulltext":false,"cited_by_count":78,"citation_normalized_percentile":{"value":0.98210736,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"29","last_page":"34"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9997000098228455,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9983999729156494,"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/semidefinite-programming","display_name":"Semidefinite programming","score":0.8305161595344543},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.7691342830657959},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6765499711036682},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6406948566436768},{"id":"https://openalex.org/keywords/semidefinite-embedding","display_name":"Semidefinite embedding","score":0.5642722249031067},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5461297631263733},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.54006028175354},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5342062711715698},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4483654201030731},{"id":"https://openalex.org/keywords/compensation","display_name":"Compensation (psychology)","score":0.4365863800048828},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40043771266937256},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30638009309768677},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.2301165759563446},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.21763485670089722}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.8305161595344543},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7691342830657959},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6765499711036682},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6406948566436768},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.5642722249031067},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5461297631263733},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.54006028175354},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5342062711715698},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4483654201030731},{"id":"https://openalex.org/C2780023022","wikidata":"https://www.wikidata.org/wiki/Q1338171","display_name":"Compensation (psychology)","level":2,"score":0.4365863800048828},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40043771266937256},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30638009309768677},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.2301165759563446},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.21763485670089722},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C11171543","wikidata":"https://www.wikidata.org/wiki/Q41630","display_name":"Psychoanalysis","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cacsd.2010.5612693","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cacsd.2010.5612693","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Symposium on Computer-Aided Control System Design","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","score":0.5699999928474426,"display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1480928214","https://openalex.org/W1964730816","https://openalex.org/W1967073510","https://openalex.org/W1979342886","https://openalex.org/W1981663184","https://openalex.org/W1988425770","https://openalex.org/W1996989380","https://openalex.org/W1999913571","https://openalex.org/W2007157764","https://openalex.org/W2012407419","https://openalex.org/W2025486357","https://openalex.org/W2060533249","https://openalex.org/W2075379600","https://openalex.org/W2090084096","https://openalex.org/W2119352997","https://openalex.org/W2120575569","https://openalex.org/W2128202699","https://openalex.org/W2752853835","https://openalex.org/W2951179629","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2385886188","https://openalex.org/W2288891047","https://openalex.org/W2524928742","https://openalex.org/W2362452378","https://openalex.org/W2353517195","https://openalex.org/W3166939022","https://openalex.org/W1727084346","https://openalex.org/W2544939111","https://openalex.org/W2386048074","https://openalex.org/W2572095861"],"abstract_inverted_index":{"Semidefinite":[0],"programming":[1,28],"(SDP)":[2],"is":[3,29],"an":[4],"important":[5],"branch":[6],"of":[7,13],"optimization":[8],"and":[9,49,55,78,100],"has":[10],"wide":[11],"range":[12],"applications:":[14],"engineering,":[15],"industry,":[16],"chemistry,":[17],"mathematics,":[18],"etc.":[19],"However,":[20],"obtaining":[21],"very":[22,82],"accurate":[23,44],"optimum":[24],"for":[25,34,96,98],"a":[26],"semidefinite":[27],"difficult":[30],"in":[31],"general,":[32],"especially":[33],"ill-posed":[35,72],"ones.":[36],"In":[37],"this":[38],"paper,":[39],"we":[40],"evaluated":[41],"numerically":[42],"highly":[43],"SDP":[45],"solvers;":[46],"SDPA-GMP,":[47,77],"-QD":[48,79],"-DD,":[50],"which":[51,69,108],"employ":[52],"multiple-precision":[53],"arithmetic":[54],"mainly":[56],"developed":[57],"by":[58],"our":[59],"group.":[60],"We":[61,102],"applied":[62],"to":[63],"some":[64,71],"problems":[65,73,81],"from":[66],"SDPLIB":[67],"benchmark":[68],"contains":[70],"as":[74],"well.":[75],"The":[76,91],"solved":[80],"accurately,":[83],"whereas":[84],"SDPA":[85],"failed":[86],"or":[87],"obtained":[88],"inaccurate":[89],"optima.":[90],"SDPA-DD":[92],"may":[93],"be":[94],"used":[95],"compensation":[97],"accuracy":[99],"speed.":[101],"also":[103],"investigated":[104],"the":[105],"convergence":[106],"behaviors":[107],"agreed":[109],"well":[110],"what":[111],"theories":[112],"indicated.":[113]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":6}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}