{"id":"https://openalex.org/W1986269781","doi":"https://doi.org/10.1137/s1064827502406658","title":"Curvilinear Linesearch for Tensor Methods","display_name":"Curvilinear Linesearch for Tensor Methods","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1986269781","doi":"https://doi.org/10.1137/s1064827502406658","mag":"1986269781"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827502406658","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502406658","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/A5110127240","display_name":"Brett W. Bader","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Brett W. Bader","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5002119487","display_name":"Robert B. Schnabel","orcid":"https://orcid.org/0000-0003-1707-0294"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert B. Schnabel","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110127240"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4713,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.76190476,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"25","issue":"2","first_page":"604","last_page":"622"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T12303","display_name":"Tensor decomposition and applications","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9887999892234802,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9800000190734863,"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/curvilinear-coordinates","display_name":"Curvilinear coordinates","score":0.7486483454704285},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6706647276878357},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5553843379020691},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4341009557247162},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4302186369895935},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32772862911224365},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1599690020084381},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07120084762573242}],"concepts":[{"id":"https://openalex.org/C98343798","wikidata":"https://www.wikidata.org/wiki/Q1790208","display_name":"Curvilinear coordinates","level":2,"score":0.7486483454704285},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6706647276878357},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5553843379020691},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4341009557247162},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4302186369895935},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32772862911224365},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1599690020084381},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07120084762573242},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1064827502406658","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502406658","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W291003596","https://openalex.org/W1580352598","https://openalex.org/W1968553199","https://openalex.org/W1983230696","https://openalex.org/W1984488466","https://openalex.org/W1993650230","https://openalex.org/W2024972953","https://openalex.org/W2039665200","https://openalex.org/W2039677328","https://openalex.org/W2056603712","https://openalex.org/W2057197834","https://openalex.org/W2068484625","https://openalex.org/W2068980859","https://openalex.org/W2136889760","https://openalex.org/W2154663204","https://openalex.org/W2164374667","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W1639593894","https://openalex.org/W63200814","https://openalex.org/W2367601375","https://openalex.org/W2371750680","https://openalex.org/W2360227361","https://openalex.org/W2067779234","https://openalex.org/W1999171692","https://openalex.org/W1600077717","https://openalex.org/W2017712750","https://openalex.org/W2382222323"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,19,29,50,56,87,120,194],"curvilinear":[4,43,135,182],"linesearch":[5,44,136],"for":[6],"use":[7,18],"when":[8,115,123],"solving":[9],"nonlinear":[10,82],"equations":[11],"with":[12,188],"tensor":[13,16,23,61,113,147,175,199],"methods.":[14],"Standard":[15],"methods":[17],"combination":[20],"of":[21,89,108,170,173,180],"the":[22,46,60,67,71,81,96,134,145,163,171,174,178,181,189],"step":[24,27,72],"and":[25,36,63,98,119,166,177],"Newton":[26,68],"in":[28,37,49],"linesearch,":[30,148],"but":[31],"they":[32],"are":[33],"handled":[34],"separately":[35],"an":[38,103],"ad":[39],"hoc":[40],"manner.":[41],"Our":[42,129],"combines":[45],"two":[47,157],"directions":[48],"single":[51],"parametric":[52],"step,":[53],"which":[54],"guarantees":[55],"monotonic":[57],"decrease":[58],"on":[59,80,86,156],"model":[62],"also":[64,131],"asymptotically":[65],"approaches":[66],"direction":[69],"as":[70],"length":[73],"shrinks":[74],"to":[75],"zero,":[76],"thus":[77],"guaranteeing":[78],"descent":[79],"equations.":[83],"Numerical":[84],"experiments":[85],"set":[88],"35":[90],"small-scale":[91,164],"problems,":[92],"drawn":[93],"primarily":[94],"from":[95],"constrained":[97],"unconstrained":[99],"testing":[100],"environment,":[101],"show":[102],"18--23%":[104],"improvement":[105,122,196],"(in":[106],"terms":[107],"function":[109],"evaluations)":[110],"over":[111,197],"previous":[112,198],"linesearches":[114],"using":[116],"quadratic":[117],"backtracking":[118],"41--83%":[121],"halving":[124],"$\\lambda$":[125],"before":[126],"each":[127],"trial.":[128],"results":[130,165],"suggest":[132],"that":[133],"is":[137],"more":[138],"robust":[139],"than":[140,152],"linesearch-based":[141],"Newton's":[142],"method":[143,176,200],"or":[144],"standard":[146],"producing":[149],"fewer":[150],"failures":[151],"either":[153],"method.":[154],"Experiments":[155],"large-scale":[158],"fluid":[159],"flow":[160],"problems":[161],"complement":[162],"give":[167],"preliminary":[168],"indication":[169],"applicability":[172],"efficiency":[179],"linesearch.":[183],"The":[184],"theoretical":[185],"properties,":[186],"coupled":[187],"better":[190],"performance,":[191],"make":[192],"this":[193],"desirable":[195],"linesearches.":[201]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
