{"id":"https://openalex.org/W2015270939","doi":"https://doi.org/10.1007/pl00005419","title":"Convergence of Newton's method for convex best interpolation","display_name":"Convergence of Newton's method for convex best interpolation","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2015270939","doi":"https://doi.org/10.1007/pl00005419","mag":"2015270939"},"language":"en","primary_location":{"id":"doi:10.1007/pl00005419","is_oa":false,"landing_page_url":"https://doi.org/10.1007/pl00005419","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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/A5083269925","display_name":"Asen L. Dontchev","orcid":"https://orcid.org/0000-0003-3160-7828"},"institutions":[{"id":"https://openalex.org/I4210159850","display_name":"Annual Reviews","ror":"https://ror.org/05r2g1b90","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210159850"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Asen L. Dontchev","raw_affiliation_strings":["Mathematical Reviews, Ann Arbor, MI 48107, USA; e-mail: ald@math.ams.org\n, , , , , , US","Mathematical Reviews, Ann Arbor, MI 48107, USA; e-mail: ald@math.ams.org , US"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Reviews, Ann Arbor, MI 48107, USA; e-mail: ald@math.ams.org\n, , , , , , US","institution_ids":["https://openalex.org/I4210159850"]},{"raw_affiliation_string":"Mathematical Reviews, Ann Arbor, MI 48107, USA; e-mail: ald@math.ams.org , US","institution_ids":["https://openalex.org/I4210159850"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112621269","display_name":"Houduo Qi","orcid":"https://orcid.org/0000-0003-3481-4814"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Houduo Qi","raw_affiliation_strings":["School of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia; e-mail: hdqi@maths.unsw.edu.au, L.Qi@unsw.edu.au\n, , , , , , AU","School of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia; e-mail: hdqi@maths.unsw.edu.au, L.Qi@unsw.edu.au , AU"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia; e-mail: hdqi@maths.unsw.edu.au, L.Qi@unsw.edu.au\n, , , , , , AU","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"School of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia; e-mail: hdqi@maths.unsw.edu.au, L.Qi@unsw.edu.au , AU","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011886900","display_name":"Liqun Qi","orcid":"https://orcid.org/0000-0002-1112-5250"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Liqun Qi","raw_affiliation_strings":["School of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia; e-mail: hdqi@maths.unsw.edu.au, L.Qi@unsw.edu.au\n, , , , , , AU","School of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia; e-mail: hdqi@maths.unsw.edu.au, L.Qi@unsw.edu.au , AU"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia; e-mail: hdqi@maths.unsw.edu.au, L.Qi@unsw.edu.au\n, , , , , , AU","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"School of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia; e-mail: hdqi@maths.unsw.edu.au, L.Qi@unsw.edu.au , AU","institution_ids":["https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":5.8695,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.96200345,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"87","issue":"3","first_page":"435","last_page":"456"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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":0.9995999932289124,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9995999932289124,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8436572551727295},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.838249683380127},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.6486250162124634},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.5580931901931763},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5031799674034119},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.49487918615341187},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4925873875617981},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.4851325452327728},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4817352592945099},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4364240765571594},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.43081676959991455},{"id":"https://openalex.org/keywords/divided-differences","display_name":"Divided differences","score":0.41955018043518066},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.414777547121048},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.40744900703430176},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34762924909591675},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.28459447622299194},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.20038112998008728},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11219647526741028},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09839046001434326},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.095787912607193}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8436572551727295},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.838249683380127},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.6486250162124634},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.5580931901931763},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5031799674034119},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.49487918615341187},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4925873875617981},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4851325452327728},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4817352592945099},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4364240765571594},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.43081676959991455},{"id":"https://openalex.org/C183554904","wikidata":"https://www.wikidata.org/wiki/Q2993265","display_name":"Divided differences","level":2,"score":0.41955018043518066},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.414777547121048},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.40744900703430176},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34762924909591675},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28459447622299194},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.20038112998008728},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11219647526741028},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09839046001434326},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.095787912607193},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/pl00005419","is_oa":false,"landing_page_url":"https://doi.org/10.1007/pl00005419","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:eprints.soton.ac.uk:29638","is_oa":false,"landing_page_url":"https://eprints.soton.ac.uk/29638/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401020","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W19099988","https://openalex.org/W1487636490","https://openalex.org/W1551360398","https://openalex.org/W1559542331","https://openalex.org/W1975466563","https://openalex.org/W1979152443","https://openalex.org/W1992688650","https://openalex.org/W1997671037","https://openalex.org/W2001508169","https://openalex.org/W2007632272","https://openalex.org/W2020084878","https://openalex.org/W2034298186","https://openalex.org/W2047668748","https://openalex.org/W2055386833","https://openalex.org/W2061872779","https://openalex.org/W2065374485","https://openalex.org/W2082746403","https://openalex.org/W2087136707","https://openalex.org/W2087236370","https://openalex.org/W2090689930","https://openalex.org/W2095586295","https://openalex.org/W2113734366","https://openalex.org/W2124959855","https://openalex.org/W2162870748"],"related_works":["https://openalex.org/W2020329095","https://openalex.org/W2075835091","https://openalex.org/W2731844756","https://openalex.org/W3048827262","https://openalex.org/W2259924831","https://openalex.org/W2741623878","https://openalex.org/W3001734434","https://openalex.org/W2083618095","https://openalex.org/W2196356369","https://openalex.org/W2035226238"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}
