{"id":"https://openalex.org/W2014855291","doi":"https://doi.org/10.1137/s1064827502406531","title":"Efficiently Computing Many Roots of a Function","display_name":"Efficiently Computing Many Roots of a Function","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2014855291","doi":"https://doi.org/10.1137/s1064827502406531","mag":"2014855291"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827502406531","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502406531","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific 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/A5111740824","display_name":"Dimitris J. Kavvadias","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"D. J. Kavvadias","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066828893","display_name":"Frosso S. Makri","orcid":"https://orcid.org/0000-0002-4438-7273"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F. S. Makri","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5044810424","display_name":"Michael N. Vrahatis","orcid":"https://orcid.org/0000-0001-8357-7435"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. N. Vrahatis","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5111740824"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.12531196,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"27","issue":"1","first_page":"93","last_page":"107"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9988999962806702,"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":0.9988999962806702,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9876000285148621,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9815999865531921,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.7756041288375854},{"id":"https://openalex.org/keywords/bisection-method","display_name":"Bisection method","score":0.6146059036254883},{"id":"https://openalex.org/keywords/simplicity","display_name":"Simplicity","score":0.5853360891342163},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5670256018638611},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.5521232485771179},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5519237518310547},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5241529941558838},{"id":"https://openalex.org/keywords/sign-function","display_name":"Sign function","score":0.5175413489341736},{"id":"https://openalex.org/keywords/preprocessor","display_name":"Preprocessor","score":0.48913314938545227},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.4534303545951843},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44300875067710876},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.43907737731933594},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4340461492538452},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2662193775177002},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12529367208480835},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1166684627532959},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08601468801498413},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07154884934425354}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7756041288375854},{"id":"https://openalex.org/C157544257","wikidata":"https://www.wikidata.org/wiki/Q866300","display_name":"Bisection method","level":2,"score":0.6146059036254883},{"id":"https://openalex.org/C2776372474","wikidata":"https://www.wikidata.org/wiki/Q508291","display_name":"Simplicity","level":2,"score":0.5853360891342163},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5670256018638611},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.5521232485771179},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5519237518310547},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5241529941558838},{"id":"https://openalex.org/C4250","wikidata":"https://www.wikidata.org/wiki/Q236813","display_name":"Sign function","level":2,"score":0.5175413489341736},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.48913314938545227},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4534303545951843},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44300875067710876},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.43907737731933594},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4340461492538452},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2662193775177002},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12529367208480835},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1166684627532959},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08601468801498413},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07154884934425354},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1064827502406531","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502406531","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.301.3545","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.301.3545","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.upatras.gr/~vrahatis/PAPERS/JOURNALS/KavvadiasMV05_SIAM_J_Sci_Comp.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":31,"referenced_works":["https://openalex.org/W1483874187","https://openalex.org/W1506829026","https://openalex.org/W1598589417","https://openalex.org/W1733230778","https://openalex.org/W1970297574","https://openalex.org/W1986919722","https://openalex.org/W1990262118","https://openalex.org/W2003860131","https://openalex.org/W2006547000","https://openalex.org/W2015773120","https://openalex.org/W2043290258","https://openalex.org/W2049088768","https://openalex.org/W2060924166","https://openalex.org/W2070055271","https://openalex.org/W2071467636","https://openalex.org/W2077490941","https://openalex.org/W2078143896","https://openalex.org/W2083087217","https://openalex.org/W2088092215","https://openalex.org/W2093105579","https://openalex.org/W2129480103","https://openalex.org/W2147559715","https://openalex.org/W2158584153","https://openalex.org/W2171295578","https://openalex.org/W2569481888","https://openalex.org/W2570659991","https://openalex.org/W2596793793","https://openalex.org/W3021898623","https://openalex.org/W3146520007","https://openalex.org/W4212820400","https://openalex.org/W4243262824"],"related_works":["https://openalex.org/W2368019753","https://openalex.org/W2333930193","https://openalex.org/W2737356002","https://openalex.org/W2246241526","https://openalex.org/W4301122218","https://openalex.org/W2374150061","https://openalex.org/W2081340182","https://openalex.org/W2369703001","https://openalex.org/W2808124387","https://openalex.org/W2350926482"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,13,16,60,87,100,125,134,143],"new":[3],"bisection":[4],"based":[5],"method":[6,20,40],"for":[7,104],"counting":[8],"and":[9,55,90],"computing":[10],"roots":[11,33,49],"of":[12,32,34,37,63,83,108,128],"function":[14,85],"in":[15,146],"given":[17],"interval.":[18],"Our":[19],"is":[21,56,74,122],"focused":[22],"on":[23],"very":[24,65],"large":[25,61],"problems,":[26],"i.e.,":[27],"instances":[28],"with":[29],"the":[30,35,45,48,75,81,84,106,109,147],"number":[31],"order":[36],"hundreds.":[38],"The":[39,120],"draws":[41],"its":[42,72,92,96,129],"power":[43],"from":[44,71],"fact":[46,76],"that":[47,77,133],"are":[50],"expected":[51],"to":[52,58,112],"be":[53,142],"many,":[54],"able":[57],"discover":[59],"percentage":[62],"them":[64],"efficiently.":[66],"Its":[67],"main":[68],"advantage,":[69],"apart":[70],"efficiency,":[73],"it":[78,99],"requires":[79],"only":[80],"sign":[82],"at":[86],"certain":[88],"point":[89],"not":[91],"actual":[93],"value.":[94],"Also,":[95],"simplicity":[97],"makes":[98],"suitable":[101],"preprocessing":[102],"step":[103],"reducing":[105],"size":[107],"problem,":[110],"prior":[111],"more":[113,117],"robust":[114],"but":[115],"also":[116],"demanding":[118],"methods.":[119],"algorithm":[121],"accompanied":[123],"by":[124],"probabilistic":[126],"analysis":[127],"behavior,":[130],"which":[131],"shows":[132],"simple":[135],"existence":[136],"criterion":[137],"like":[138],"Bolzano's":[139],"rule":[140],"can":[141],"powerful":[144],"tool":[145],"zerofinding":[148],"process.":[149]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}