{"id":"https://openalex.org/W3026480211","doi":"https://doi.org/10.1145/3386241","title":"Algorithm 1010","display_name":"Algorithm 1010","publication_year":2020,"publication_date":"2020-05-19","ids":{"openalex":"https://openalex.org/W3026480211","doi":"https://doi.org/10.1145/3386241","mag":"3026480211"},"language":"en","primary_location":{"id":"doi:10.1145/3386241","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3386241","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","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/A5049413235","display_name":"Alberto Giacomo Orellana","orcid":null},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alberto Giacomo Orellana","raw_affiliation_strings":["Dipartimento di Fisica, \u201cSapienza\u201d Universit\u00e0 di Roma, Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Fisica, \u201cSapienza\u201d Universit\u00e0 di Roma, Rome, Italy","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063297991","display_name":"Cristiano De Michele","orcid":"https://orcid.org/0000-0002-8367-0610"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Cristiano De Michele","raw_affiliation_strings":["Dipartimento di Fisica, \u201cSapienza\u201d Universit\u00e0 di Roma, Rome, Italy"],"raw_orcid":"https://orcid.org/0000-0002-8367-0610","affiliations":[{"raw_affiliation_string":"Dipartimento di Fisica, \u201cSapienza\u201d Universit\u00e0 di Roma, Rome, Italy","institution_ids":["https://openalex.org/I861853513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.61,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.63605169,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"46","issue":"2","first_page":"1","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10402","display_name":"Phase Equilibria and Thermodynamics","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10402","display_name":"Phase Equilibria and Thermodynamics","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9930999875068665,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9912999868392944,"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/quartic-function","display_name":"Quartic function","score":0.85439133644104},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.782150387763977},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5987959504127502},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5551648736000061},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5499375462532043},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5282926559448242},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49271705746650696},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4813581109046936},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4284718334674835},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35005396604537964},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09553825855255127}],"concepts":[{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.85439133644104},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.782150387763977},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5987959504127502},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5551648736000061},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5499375462532043},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5282926559448242},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49271705746650696},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4813581109046936},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4284718334674835},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35005396604537964},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09553825855255127},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3386241","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3386241","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},{"id":"pmh:oai:iris.uniroma1.it:11573/1571217","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/1571217","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W200391750","https://openalex.org/W1524943583","https://openalex.org/W1570448469","https://openalex.org/W1673177621","https://openalex.org/W1832583097","https://openalex.org/W1861750978","https://openalex.org/W1964217018","https://openalex.org/W1969724681","https://openalex.org/W1984584165","https://openalex.org/W1990024658","https://openalex.org/W1990749444","https://openalex.org/W1991931792","https://openalex.org/W1996478441","https://openalex.org/W2000495980","https://openalex.org/W2008476021","https://openalex.org/W2012893647","https://openalex.org/W2013814296","https://openalex.org/W2014979769","https://openalex.org/W2023212766","https://openalex.org/W2026808905","https://openalex.org/W2028994765","https://openalex.org/W2030755808","https://openalex.org/W2031405809","https://openalex.org/W2037061816","https://openalex.org/W2046051750","https://openalex.org/W2050295070","https://openalex.org/W2054004284","https://openalex.org/W2054629786","https://openalex.org/W2057832664","https://openalex.org/W2059755511","https://openalex.org/W2069506715","https://openalex.org/W2070902971","https://openalex.org/W2075649813","https://openalex.org/W2080830113","https://openalex.org/W2088387238","https://openalex.org/W2090960299","https://openalex.org/W2105177045","https://openalex.org/W2117640700","https://openalex.org/W2120204404","https://openalex.org/W2125938106","https://openalex.org/W2130818188","https://openalex.org/W2137878433","https://openalex.org/W2141100342","https://openalex.org/W2159957588","https://openalex.org/W2187028849","https://openalex.org/W2237268071","https://openalex.org/W2255365989","https://openalex.org/W2264560318","https://openalex.org/W2268792413","https://openalex.org/W2320426448","https://openalex.org/W2604736346","https://openalex.org/W2622307122","https://openalex.org/W2626345811","https://openalex.org/W2797073647","https://openalex.org/W3101927247","https://openalex.org/W3104895996","https://openalex.org/W3105080255","https://openalex.org/W3174319433","https://openalex.org/W4231219113","https://openalex.org/W4240120430","https://openalex.org/W6692223624"],"related_works":["https://openalex.org/W2000297171","https://openalex.org/W2777256819","https://openalex.org/W4221159894","https://openalex.org/W4297058887","https://openalex.org/W4307280152","https://openalex.org/W4225346682","https://openalex.org/W4288563609","https://openalex.org/W4249930925","https://openalex.org/W4299284326","https://openalex.org/W2055833800"],"abstract_inverted_index":{"Aiming":[0],"to":[1,91,96,114,146],"provide":[2],"a":[3,133,161,165,179],"very":[4,70,93,166],"accurate,":[5],"efficient,":[6],"and":[7,29,57,157],"robust":[8],"quartic":[9,41,128,148],"equation":[10,149],"solver":[11],"for":[12,103],"physical":[13,180],"applications,":[14],"we":[15,139],"have":[16],"proposed":[17],"an":[18],"algorithm":[19,68,143,172],"that":[20,78],"builds":[21],"on":[22,36],"the":[23,37,40,61,64,83,106,109,117],"previous":[24],"works":[25],"of":[26,39,63,108,120,127,169,184],"P.":[27],"Strobach":[28],"S.":[30],"L.":[31],"Shmakov.":[32],"It":[33],"is":[34,69,105,130],"based":[35],"decomposition":[38],"polynomial":[42],"into":[43],"two":[44],"quadratics,":[45],"whose":[46],"coefficients":[47,129],"are":[48],"first":[49],"accurately":[50],"estimated":[51],"by":[52,152,158],"handling":[53],"carefully":[54],"numerical":[55],"errors":[56],"afterward":[58],"refined":[59],"through":[60],"use":[62],"Newton-Raphson":[65],"method.":[66],"Our":[67,171],"accurate":[71],"in":[72,82,132,144,178],"comparison":[73,145],"with":[74,116],"other":[75,147],"state-of-the-art":[76],"solvers":[77,150],"can":[79],"be":[80,92],"found":[81],"literature,":[84],"but":[85],"(most":[86],"importantly)":[87],"it":[88,188],"turns":[89],"out":[90,160],"efficient":[94],"according":[95],"our":[97,142],"timing":[98],"tests.":[99],"A":[100],"crucial":[101],"issue":[102],"us":[104],"robustness":[107],"algorithm,":[110],"i.e.,":[111,182],"its":[112,190,196],"ability":[113],"cope":[115],"detrimental":[118],"effect":[119],"round-off":[121],"errors,":[122],"no":[123],"matter":[124],"what":[125],"set":[126,168],"provided":[131],"practical":[134],"application.":[135],"In":[136],"this":[137],"respect,":[138],"extensively":[140],"tested":[141,177],"both":[151],"considering":[153],"specific":[154],"extreme":[155],"cases":[156],"carrying":[159],"statistical":[162],"analysis":[163],"over":[164],"large":[167],"quartics.":[170],"has":[173],"also":[174],"been":[175],"heavily":[176],"application,":[181],"simulations":[183],"hard":[185],"cylinders,":[186],"where":[187],"proved":[189],"absolute":[191],"reliability":[192],"as":[193,195],"well":[194],"efficiency.":[197]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2020-05-29T00:00:00"}