{"id":"https://openalex.org/W1988420021","doi":"https://doi.org/10.1080/00207160802275951","title":"Applications of the Conjugate Gradient method in optimal surface parameterizations","display_name":"Applications of the Conjugate Gradient method in optimal surface parameterizations","publication_year":2008,"publication_date":"2008-10-14","ids":{"openalex":"https://openalex.org/W1988420021","doi":"https://doi.org/10.1080/00207160802275951","mag":"1988420021"},"language":"en","primary_location":{"id":"doi:10.1080/00207160802275951","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160802275951","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/A5075378610","display_name":"Zhongxiao Jia","orcid":"https://orcid.org/0000-0001-9761-8517"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhongxiao Jia","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University , Beijing, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University , Beijing, People's Republic of China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075378610"],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.06564275,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"87","issue":"5","first_page":"1032","last_page":"1039"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9962999820709229,"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"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.8422625064849854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6013603806495667},{"id":"https://openalex.org/keywords/mathematics-subject-classification","display_name":"Mathematics Subject Classification","score":0.5523843169212341},{"id":"https://openalex.org/keywords/christian-ministry","display_name":"Christian ministry","score":0.5369853973388672},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.524880588054657},{"id":"https://openalex.org/keywords/subject","display_name":"Subject (documents)","score":0.4581207036972046},{"id":"https://openalex.org/keywords/derivation-of-the-conjugate-gradient-method","display_name":"Derivation of the conjugate gradient method","score":0.45685794949531555},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.45151710510253906},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4396592378616333},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.4371935725212097},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3827058970928192},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37612462043762207},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3469662368297577},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3227471113204956},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25949162244796753},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.21219933032989502},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17392566800117493},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12173900008201599},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11030572652816772},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.0800398588180542}],"concepts":[{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.8422625064849854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6013603806495667},{"id":"https://openalex.org/C2778778035","wikidata":"https://www.wikidata.org/wiki/Q967960","display_name":"Mathematics Subject Classification","level":2,"score":0.5523843169212341},{"id":"https://openalex.org/C521751864","wikidata":"https://www.wikidata.org/wiki/Q1729207","display_name":"Christian ministry","level":2,"score":0.5369853973388672},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.524880588054657},{"id":"https://openalex.org/C2777855551","wikidata":"https://www.wikidata.org/wiki/Q12310021","display_name":"Subject (documents)","level":2,"score":0.4581207036972046},{"id":"https://openalex.org/C198562538","wikidata":"https://www.wikidata.org/wiki/Q5262612","display_name":"Derivation of the conjugate gradient method","level":5,"score":0.45685794949531555},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.45151710510253906},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4396592378616333},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.4371935725212097},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3827058970928192},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37612462043762207},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3469662368297577},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3227471113204956},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25949162244796753},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.21219933032989502},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17392566800117493},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12173900008201599},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11030572652816772},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0800398588180542},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/C161191863","wikidata":"https://www.wikidata.org/wiki/Q199655","display_name":"Library science","level":1,"score":0.0},{"id":"https://openalex.org/C27206212","wikidata":"https://www.wikidata.org/wiki/Q34178","display_name":"Theology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160802275951","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160802275951","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1975434639","https://openalex.org/W2018850201","https://openalex.org/W2034775820","https://openalex.org/W2134427293","https://openalex.org/W2143897237","https://openalex.org/W2798909945"],"related_works":["https://openalex.org/W2009461808","https://openalex.org/W2068685638","https://openalex.org/W81845748","https://openalex.org/W2035892225","https://openalex.org/W2365504875","https://openalex.org/W3188682559","https://openalex.org/W2049036377","https://openalex.org/W2896548519","https://openalex.org/W2975512210","https://openalex.org/W1976157534"],"abstract_inverted_index":{"AbstractThis":[0],"paper":[1,102],"concerns":[2],"the":[3,16,32,47,71,108,114,120,128,132],"solutions":[4],"of":[5,18,39,110,131,134],"very":[6,75],"large":[7,66],"symmetric":[8,40,77],"semipositive":[9],"definite":[10,42],"(singular)":[11],"linear":[12,34,43],"systems":[13,35],"involved":[14],"in":[15,99],"problem":[17,115],"optimal":[19],"surface":[20],"parameterizations":[21],"using":[22],"inverse":[23],"curvature":[24],"mapping.":[25],"Two":[26],"approaches":[27],"are":[28,61],"presented":[29],"that":[30,46,70,97],"transform":[31],"singular":[33],"into":[36],"two":[37,64,89],"kinds":[38],"positive":[41],"systems,":[44],"so":[45],"famous":[48],"Conjugate":[49],"Gradient":[50],"(CG)":[51],"method":[52],"can":[53],"be":[54],"used":[55],"for":[56,91,112],"solving":[57],"them.":[58],"Numerical":[59],"experiments":[60],"run":[62],"on":[63],"practical":[65],"problems":[67],"to":[68,107],"illustrate":[69],"CG":[72],"algorithm":[73],"works":[74],"efficiently.Keywords:":[76],"seimidefinitepositive":[78],"definiteCGKrylov":[79],"subspacesurface":[80],"parameterization2000":[81],"AMS":[82],"Subject":[83],"Classification::":[84],"65F1065D1768U07":[85],"AcknowledgementsThe":[86],"author":[87],"thanks":[88],"referees":[90],"their":[92],"valuable":[93],"comments":[94],"and":[95,116,127],"suggestions":[96],"helped":[98],"improving":[100],"this":[101],"considerably.":[103],"Thanks":[104],"also":[105],"go":[106],"authors":[109],"Citation7":[111],"providing":[113],"data.":[117],"Supported":[118],"by":[119],"National":[121],"Natural":[122],"Science":[123],"Foundation":[124],"(No.":[125,136],"10771116)":[126],"Doctoral":[129],"Program":[130],"Ministry":[133],"Education":[135],"20060003003).":[137]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}