{"id":"https://openalex.org/W306081428","doi":"https://doi.org/10.1007/s11075-015-9980-y","title":"Presentation of a highly tuned multithreaded interval solver for underdetermined and well-determined nonlinear systems","display_name":"Presentation of a highly tuned multithreaded interval solver for underdetermined and well-determined nonlinear systems","publication_year":2015,"publication_date":"2015-03-23","ids":{"openalex":"https://openalex.org/W306081428","doi":"https://doi.org/10.1007/s11075-015-9980-y","mag":"306081428"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-015-9980-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-015-9980-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-015-9980-y.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11075-015-9980-y.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002291613","display_name":"Bart\u0142omiej Jacek Kubica","orcid":"https://orcid.org/0000-0002-5547-3759"},"institutions":[{"id":"https://openalex.org/I108403487","display_name":"Warsaw University of Technology","ror":"https://ror.org/00y0xnp53","country_code":"PL","type":"education","lineage":["https://openalex.org/I108403487"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Bart\u0142omiej Jacek Kubica","raw_affiliation_strings":["Institute of Control and Computation Engineering, Warsaw University of Technology, Nowowiejska 15/19, 00-665, Warsaw, Poland","Institute of Control and Computation Engineering, Warsaw University of Technology,Warsaw,Poland,00-665"],"affiliations":[{"raw_affiliation_string":"Institute of Control and Computation Engineering, Warsaw University of Technology, Nowowiejska 15/19, 00-665, Warsaw, Poland","institution_ids":["https://openalex.org/I108403487"]},{"raw_affiliation_string":"Institute of Control and Computation Engineering, Warsaw University of Technology,Warsaw,Poland,00-665","institution_ids":["https://openalex.org/I108403487"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002291613"],"corresponding_institution_ids":["https://openalex.org/I108403487"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.4892,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.81508159,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"70","issue":"4","first_page":"929","last_page":"963"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":1.0,"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/T11697","display_name":"Numerical Methods and Algorithms","score":1.0,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/solver","display_name":"Solver","score":0.8101190328598022},{"id":"https://openalex.org/keywords/underdetermined-system","display_name":"Underdetermined system","score":0.7216432094573975},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6886003017425537},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6350628733634949},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.611040472984314},{"id":"https://openalex.org/keywords/bisection-method","display_name":"Bisection method","score":0.5973044633865356},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5597598552703857},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5492916703224182},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5058257579803467},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.4671361446380615},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.46364203095436096},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.4594271183013916},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45488524436950684},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38268154859542847},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.333972692489624},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33135151863098145},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10818111896514893},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07473328709602356},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.074485182762146}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.8101190328598022},{"id":"https://openalex.org/C179690561","wikidata":"https://www.wikidata.org/wiki/Q4316110","display_name":"Underdetermined system","level":2,"score":0.7216432094573975},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6886003017425537},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6350628733634949},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.611040472984314},{"id":"https://openalex.org/C157544257","wikidata":"https://www.wikidata.org/wiki/Q866300","display_name":"Bisection method","level":2,"score":0.5973044633865356},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5597598552703857},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5492916703224182},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5058257579803467},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.4671361446380615},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.46364203095436096},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.4594271183013916},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45488524436950684},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38268154859542847},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.333972692489624},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33135151863098145},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10818111896514893},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07473328709602356},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.074485182762146},{"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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":1,"locations":[{"id":"doi:10.1007/s11075-015-9980-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-015-9980-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-015-9980-y.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11075-015-9980-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-015-9980-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-015-9980-y.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8299999833106995,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W306081428.pdf","grobid_xml":"https://content.openalex.org/works/W306081428.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W22398292","https://openalex.org/W57462620","https://openalex.org/W271412832","https://openalex.org/W850734834","https://openalex.org/W1530296569","https://openalex.org/W1563516866","https://openalex.org/W1564384322","https://openalex.org/W1578845863","https://openalex.org/W1588693185","https://openalex.org/W1734024950","https://openalex.org/W1854695584","https://openalex.org/W1867321338","https://openalex.org/W1966153504","https://openalex.org/W1995960064","https://openalex.org/W2020619471","https://openalex.org/W2021221313","https://openalex.org/W2032648441","https://openalex.org/W2055604481","https://openalex.org/W2067648572","https://openalex.org/W2067783185","https://openalex.org/W2073787328","https://openalex.org/W2076061149","https://openalex.org/W2087743687","https://openalex.org/W2129480103","https://openalex.org/W2145696022","https://openalex.org/W2396920442","https://openalex.org/W2399505145","https://openalex.org/W2549082795","https://openalex.org/W3146520007"],"related_works":["https://openalex.org/W176802781","https://openalex.org/W2997320962","https://openalex.org/W4287906532","https://openalex.org/W3011121006","https://openalex.org/W2080845659","https://openalex.org/W126544226","https://openalex.org/W3158611816","https://openalex.org/W2153862782","https://openalex.org/W1988522734","https://openalex.org/W2808124387"],"abstract_inverted_index":{"The":[0],"paper":[1],"summarizes":[2],"author\u2019s":[3],"investigations":[4],"in":[5],"tuning":[6],"a":[7,29,40],"multithreaded":[8],"interval":[9],"branch-and-prune":[10],"algorithm":[11],"for":[12,22,47],"nonlinear":[13],"systems":[14],"and":[15,28],"presents":[16],"the":[17,24,33,45,58,62],"developed":[18],"solver.":[19],"New":[20],"results":[21],"using":[23],"box-consistency":[25],"enforcing":[26],"operator":[27],"new":[30,41],"variant":[31],"of":[32,61],"initial":[34],"exclusion":[35],"phase":[36],"are":[37,54],"presented.":[38],"Also,":[39],"heuristic":[42],"to":[43,56],"choose":[44],"coordinate":[46],"bisection":[48],"is":[49],"considered.":[50],"Extensive":[51],"numerical":[52],"experiments":[53],"analyzed":[55],"provide":[57],"satisfying":[59],"version":[60],"algorithm.":[63]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
