{"id":"https://openalex.org/W4245254698","doi":"https://doi.org/10.1080/00207169508804378","title":"A new dimension\u2014reducing method for solving systems of nonlinear equations","display_name":"A new dimension\u2014reducing method for solving systems of nonlinear equations","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W4245254698","doi":"https://doi.org/10.1080/00207169508804378"},"language":"en","primary_location":{"id":"doi:10.1080/00207169508804378","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169508804378","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/A5025128776","display_name":"T. N. Grapsa","orcid":null},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"T. N. Grapsa","raw_affiliation_strings":["Department of Mathematics , University of Patras , Patras, GR-261.10,  Greece"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Patras , Patras, GR-261.10,  Greece","institution_ids":["https://openalex.org/I174878644"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044810424","display_name":"Michael N. Vrahatis","orcid":"https://orcid.org/0000-0001-8357-7435"},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"M. N. Vrahatis","raw_affiliation_strings":["Department of Mathematics , University of Patras , Patras, GR-261.10,  Greece"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Patras , Patras, GR-261.10,  Greece","institution_ids":["https://openalex.org/I174878644"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025128776"],"corresponding_institution_ids":["https://openalex.org/I174878644"],"apc_list":null,"apc_paid":null,"fwci":1.0981,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.79369369,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"55","issue":"3-4","first_page":"235","last_page":"244"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential 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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential 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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9984999895095825,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8145933151245117},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5729414224624634},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5710799694061279},{"id":"https://openalex.org/keywords/transcendental-equation","display_name":"Transcendental equation","score":0.5596978664398193},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.5592129230499268},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5346172451972961},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.5160367488861084},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.501000165939331},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4507187008857727},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4445610046386719},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4353882670402527},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.4299823045730591},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.42704272270202637},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.4123413562774658},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.3797684907913208},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3181306719779968},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2946724593639374},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2242521345615387}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8145933151245117},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5729414224624634},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5710799694061279},{"id":"https://openalex.org/C139609574","wikidata":"https://www.wikidata.org/wiki/Q2273509","display_name":"Transcendental equation","level":3,"score":0.5596978664398193},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.5592129230499268},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5346172451972961},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.5160367488861084},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.501000165939331},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4507187008857727},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4445610046386719},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4353882670402527},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.4299823045730591},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.42704272270202637},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.4123413562774658},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3797684907913208},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3181306719779968},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2946724593639374},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2242521345615387},{"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169508804378","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169508804378","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W141715888","https://openalex.org/W1988193272","https://openalex.org/W2056603712","https://openalex.org/W2065872032","https://openalex.org/W2074765826","https://openalex.org/W2343728241","https://openalex.org/W4297926604"],"related_works":["https://openalex.org/W3213335643","https://openalex.org/W2141137682","https://openalex.org/W2762148993","https://openalex.org/W2769625221","https://openalex.org/W2376043095","https://openalex.org/W3201369084","https://openalex.org/W2029986120","https://openalex.org/W2048880201","https://openalex.org/W1987393399","https://openalex.org/W2003288928"],"abstract_inverted_index":{"A":[0,140],"new":[1],"method":[2,22],"for":[3,42,115],"the":[4,24,27,43,51,57,69,75,79,98,104,119],"numerical":[5,147],"solution":[6,52,70,120],"of":[7,9,26,45,50,68,78,89,103,118,142],"systems":[8],"nonlinear":[10],"algebraic":[11],"and/or":[12],"transcendental":[13],"equations":[14],"in":[15,29,91],"R":[16,92],"n":[17,46,99],"is":[18,71,144],"presented.":[19,150],"Firstly,":[20],"this":[21],"reduces":[23],"dimensionality":[25],"system":[28],"such":[30],"a":[31,87,111],"way":[32],"that":[33],"it":[34,55,107,122,130],"can":[35,131],"lead":[36],"to":[37,97,134],"an":[38],"iterative":[39,84],"approximate":[40],"formula":[41,85],"computation":[44],"\u2212":[47,100],"1":[48,101],"components":[49,102],"and":[53,121,146],"subsequently":[54],"perturbs":[56],"corresponding":[58],"Jacobian":[59],"by":[60],"using":[61,74],"proper":[62],"perturbation":[63],"parameters.":[64],"The":[65],"remaining":[66],"component":[67,117],"evaluated":[72],"separately":[73],"final":[76],"approximations":[77],"other":[80],"components.":[81],"This":[82],"reduced":[83],"generates":[86],"sequence":[88],"points":[90],"n\u22121":[93],"which":[94],"converges":[95],"quadratically":[96],"solution.":[105],"Moreover,":[106],"does":[108,123],"not":[109,124],"require":[110],"good":[112],"initial":[113],"guess":[114],"one":[116],"directly":[125],"perform":[126],"function":[127,138],"evaluations.":[128],"Thus,":[129],"be":[132],"applied":[133],"problems":[135],"with":[136],"imprecise":[137],"values.":[139],"proof":[141],"convergence":[143],"given":[145],"applications":[148],"are":[149]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
