{"id":"https://openalex.org/W2075341408","doi":"https://doi.org/10.1137/090758763","title":"On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency","display_name":"On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2075341408","doi":"https://doi.org/10.1137/090758763","mag":"2075341408"},"language":"en","primary_location":{"id":"doi:10.1137/090758763","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090758763","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5101857910","display_name":"Miodrag S. Petkovi\u0107","orcid":"https://orcid.org/0000-0002-6799-7912"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Miodrag S. Petkovi\u0107","raw_affiliation_strings":["msp@junis.ni.ac.rs#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"msp@junis.ni.ac.rs#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5101857910"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":24.1519,"has_fulltext":false,"cited_by_count":102,"citation_normalized_percentile":{"value":0.99862511,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"47","issue":"6","first_page":"4402","last_page":"4414"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":1.0,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":1.0,"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":0.9933000206947327,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9821000099182129,"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/mathematics","display_name":"Mathematics","score":0.8513331413269043},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7166415452957153},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.651375412940979},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.6250988841056824},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5609853267669678},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5416988730430603},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.52643883228302},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4727557301521301},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.451462060213089},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.4445570111274719},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.44062697887420654},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.43180951476097107},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2705775201320648},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10795745253562927},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0981256365776062}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8513331413269043},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7166415452957153},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.651375412940979},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6250988841056824},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5609853267669678},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5416988730430603},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.52643883228302},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4727557301521301},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.451462060213089},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.4445570111274719},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.44062697887420654},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.43180951476097107},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2705775201320648},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10795745253562927},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0981256365776062},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090758763","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090758763","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W824181044","https://openalex.org/W1499223973","https://openalex.org/W1972417972","https://openalex.org/W1975400766","https://openalex.org/W1977711281","https://openalex.org/W1998140106","https://openalex.org/W2026091072","https://openalex.org/W2041343963","https://openalex.org/W2044487944","https://openalex.org/W2048632019","https://openalex.org/W2055308255","https://openalex.org/W2055607857","https://openalex.org/W2068000066","https://openalex.org/W2069144579","https://openalex.org/W2070251772","https://openalex.org/W2075308367"],"related_works":["https://openalex.org/W2377857862","https://openalex.org/W2358591430","https://openalex.org/W2350788688","https://openalex.org/W2351377961","https://openalex.org/W2357287617","https://openalex.org/W2103912232","https://openalex.org/W2562964647","https://openalex.org/W3140142921","https://openalex.org/W4311074794","https://openalex.org/W4308670056"],"abstract_inverted_index":{"A":[0],"general":[1],"class":[2,57,83],"of":[3,16,24,28,58,70,73,94],"n-point":[4],"iterative":[5],"methods":[6,15,35,59,75],"for":[7],"solving":[8],"nonlinear":[9],"equations":[10],"is":[11,31,52],"constructed":[12],"by":[13],"combining":[14],"Newton's":[17],"type":[18],"and":[19],"an":[20],"arbitrary":[21],"two-point":[22],"method":[23],"the":[25,37,55,61,66,71,92,95],"fourth":[26],"order":[27,39,72],"convergence.":[29],"It":[30],"proved":[32],"that":[33,54],"these":[34],"have":[36],"convergence":[38,105],"$2^n$,":[40],"requiring":[41],"only":[42,108],"$n+1$":[43,78],"function":[44,79,110],"evaluations":[45],"per":[46],"iteration.":[47],"In":[48],"this":[49,82],"way":[50],"it":[51],"demonstrated":[53],"proposed":[56],"supports":[60],"Kung\u2013Traub":[62,96],"hypothesis":[63],"(1974)":[64],"on":[65,77],"upper":[67],"bound":[68],"$2^n$":[69],"multipoint":[74],"based":[76],"evaluations.":[80,111],"Consequently,":[81],"possess":[84],"as":[85,87],"high":[86],"possible":[88],"computational":[89],"efficiency":[90],"in":[91],"sense":[93],"hypothesis.":[97],"Numerical":[98],"examples":[99],"are":[100],"included":[101],"to":[102],"demonstrate":[103],"exceptional":[104],"speed":[106],"with":[107],"few":[109]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":20}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}