{"id":"https://openalex.org/W2040670322","doi":"https://doi.org/10.1080/00207161003770386","title":"A new gradient method via least change secant update","display_name":"A new gradient method via least change secant update","publication_year":2010,"publication_date":"2010-12-23","ids":{"openalex":"https://openalex.org/W2040670322","doi":"https://doi.org/10.1080/00207161003770386","mag":"2040670322"},"language":"en","primary_location":{"id":"doi:10.1080/00207161003770386","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207161003770386","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5101855246","display_name":"Wah June Leong","orcid":"https://orcid.org/0000-0003-3149-4210"},"institutions":[{"id":"https://openalex.org/I130343225","display_name":"Universiti Putra Malaysia","ror":"https://ror.org/02e91jd64","country_code":"MY","type":"education","lineage":["https://openalex.org/I130343225"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Wah June Leong","raw_affiliation_strings":["Department of Mathematics , University Putra Malaysia , 43400, Serdang, Selangor, Malaysia","Department of Mathematics, University Putra Malaysia, Serdang, Selangor, Malaysia;"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University Putra Malaysia , 43400, Serdang, Selangor, Malaysia","institution_ids":["https://openalex.org/I130343225"]},{"raw_affiliation_string":"Department of Mathematics, University Putra Malaysia, Serdang, Selangor, Malaysia;","institution_ids":["https://openalex.org/I130343225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100818089","display_name":"Malik Abu Hassan","orcid":null},"institutions":[{"id":"https://openalex.org/I130343225","display_name":"Universiti Putra Malaysia","ror":"https://ror.org/02e91jd64","country_code":"MY","type":"education","lineage":["https://openalex.org/I130343225"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Malik Abu Hassan","raw_affiliation_strings":["Department of Mathematics , University Putra Malaysia , 43400, Serdang, Selangor, Malaysia","Department of Mathematics, University Putra Malaysia, Serdang, Selangor, Malaysia;"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University Putra Malaysia , 43400, Serdang, Selangor, Malaysia","institution_ids":["https://openalex.org/I130343225"]},{"raw_affiliation_string":"Department of Mathematics, University Putra Malaysia, Serdang, Selangor, Malaysia;","institution_ids":["https://openalex.org/I130343225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101855246"],"corresponding_institution_ids":["https://openalex.org/I130343225"],"apc_list":null,"apc_paid":null,"fwci":1.8794,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.85129018,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"88","issue":"4","first_page":"816","last_page":"828"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9997000098228455,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":0.750713050365448},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.7324960231781006},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.7040665149688721},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.6515406370162964},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.6061567664146423},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5539160370826721},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5460077524185181},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5331399440765381},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.5027966499328613},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.4607582688331604},{"id":"https://openalex.org/keywords/secant-method","display_name":"Secant method","score":0.4494938850402832},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4311755299568176},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4171915054321289},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.3957221806049347},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37434273958206177},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2848683297634125},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2082127332687378},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19313934445381165},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14647552371025085}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.750713050365448},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.7324960231781006},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.7040665149688721},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.6515406370162964},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.6061567664146423},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5539160370826721},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5460077524185181},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5331399440765381},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.5027966499328613},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.4607582688331604},{"id":"https://openalex.org/C93926214","wikidata":"https://www.wikidata.org/wiki/Q14915286","display_name":"Secant method","level":4,"score":0.4494938850402832},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4311755299568176},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4171915054321289},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.3957221806049347},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37434273958206177},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2848683297634125},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2082127332687378},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19313934445381165},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14647552371025085},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207161003770386","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207161003770386","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:psasir.upm.edu.my:12746","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196260","display_name":"Universiti Putra Malaysia Institutional Repository (Universiti Putra Malaysia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130343225","host_organization_name":"Universiti Putra Malaysia","host_organization_lineage":["https://openalex.org/I130343225"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321784","display_name":"Kementerian Sains, Teknologi dan Inovasi","ror":"https://ror.org/012s3r374"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W129805247","https://openalex.org/W173320072","https://openalex.org/W1497566274","https://openalex.org/W1988849934","https://openalex.org/W2005724054","https://openalex.org/W2038210983","https://openalex.org/W2039771911","https://openalex.org/W2050096287","https://openalex.org/W2062106836","https://openalex.org/W2069828243","https://openalex.org/W2076605490","https://openalex.org/W2085694061","https://openalex.org/W2316564661","https://openalex.org/W2340930132"],"related_works":["https://openalex.org/W2356977358","https://openalex.org/W2381924799","https://openalex.org/W2183734858","https://openalex.org/W4319027779","https://openalex.org/W2349115186","https://openalex.org/W2355555245","https://openalex.org/W2384571804","https://openalex.org/W2962081168","https://openalex.org/W4233179678","https://openalex.org/W2130355210"],"abstract_inverted_index":{"The":[0],"Barzilai\u2013Borwein":[1],"(BB)":[2],"gradient":[3,76,86],"method":[4,12,21,77,87],"is":[5,94],"favourable":[6],"over":[7],"the":[8,48,52,56,60,69,81,90],"classical":[9],"steepest":[10],"descent":[11],"both":[13],"in":[14,17,88],"theory":[15],"and":[16,72],"real":[18],"computations.":[19],"This":[20],"takes":[22],"a":[23,30,44,63,74,97],"\u2018fixed\u2019":[24],"step":[25,99],"size":[26],"rather":[27],"than":[28],"following":[29],"set":[31],"of":[32,62,84],"line":[33,91],"search":[34,92],"rules":[35],"to":[36,51,80],"ensure":[37],"convergence.":[38],"Along":[39],"this":[40],"line,":[41],"we":[42],"present":[43],"new":[45,75],"approach":[46],"for":[47,68],"two-point":[49],"approximation":[50],"quasi-Newton":[53],"equation":[54],"within":[55],"BB":[57,85],"framework":[58],"on":[59],"basis":[61],"well-known":[64],"least":[65],"change":[66],"result":[67],"Davidon\u2013Fletcher\u2013Powell":[70],"update":[71],"propose":[73],"that":[78,106],"belongs":[79],"same":[82],"class":[83],"which":[89],"procedure":[93],"replaced":[95],"by":[96],"fixed":[98],"size.":[100],"Some":[101],"preliminary":[102],"numerical":[103],"results":[104],"suggest":[105],"improvements":[107],"have":[108],"been":[109],"achieved.":[110]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}