{"id":"https://openalex.org/W1989131020","doi":"https://doi.org/10.1137/s0036142902419600","title":"Fast Sweeping Methods for Static Hamilton--Jacobi Equations","display_name":"Fast Sweeping Methods for Static Hamilton--Jacobi Equations","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1989131020","doi":"https://doi.org/10.1137/s0036142902419600","mag":"1989131020"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142902419600","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902419600","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5045327320","display_name":"Chiu\u2010Yen Kao","orcid":"https://orcid.org/0000-0003-3082-4943"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chiu-Yen Kao","raw_affiliation_strings":["University of California\u2013Los Angeles"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California\u2013Los Angeles","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002037883","display_name":"Stanley Osher","orcid":"https://orcid.org/0000-0002-7900-4658"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stanley Osher","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108538101","display_name":"Yen-Hsi Tsai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yen-Hsi Tsai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":15.995,"has_fulltext":false,"cited_by_count":141,"citation_normalized_percentile":{"value":0.99535871,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"42","issue":"6","first_page":"2612","last_page":"2632"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987000226974487,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9961000084877014,"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/legendre-polynomials","display_name":"Legendre polynomials","score":0.8549885749816895},{"id":"https://openalex.org/keywords/legendre-transformation","display_name":"Legendre transformation","score":0.7962260842323303},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7851294279098511},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.713346004486084},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.5753179788589478},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5701754689216614},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5550890564918518},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.516075074672699},{"id":"https://openalex.org/keywords/legendre-wavelet","display_name":"Legendre wavelet","score":0.5088134407997131},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4809074401855469},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.43929535150527954},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.43398991227149963},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39267498254776},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2990446090698242},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1561301350593567},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14088410139083862}],"concepts":[{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.8549885749816895},{"id":"https://openalex.org/C116594300","wikidata":"https://www.wikidata.org/wiki/Q908652","display_name":"Legendre transformation","level":2,"score":0.7962260842323303},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7851294279098511},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.713346004486084},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.5753179788589478},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5701754689216614},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5550890564918518},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.516075074672699},{"id":"https://openalex.org/C123769847","wikidata":"https://www.wikidata.org/wiki/Q6517888","display_name":"Legendre wavelet","level":5,"score":0.5088134407997131},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4809074401855469},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.43929535150527954},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.43398991227149963},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39267498254776},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2990446090698242},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1561301350593567},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14088410139083862},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.0},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0036142902419600","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902419600","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.409.2553","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.409.2553","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.nus.edu.sg/~bao/teach/ma5233/so2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.6.3537","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.3537","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.math.ucla.edu/pub/camreport/cam03-75.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.8.1447","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.8.1447","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.math.ucla.edu/pub/camreport/cam02-66.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W153353184","https://openalex.org/W1986838484","https://openalex.org/W1991113069","https://openalex.org/W1994015146","https://openalex.org/W1996204208","https://openalex.org/W1999690352","https://openalex.org/W2000359198","https://openalex.org/W2003009438","https://openalex.org/W2005126631","https://openalex.org/W2006969491","https://openalex.org/W2012872284","https://openalex.org/W2014405238","https://openalex.org/W2021513670","https://openalex.org/W2025237803","https://openalex.org/W2027438381","https://openalex.org/W2027689502","https://openalex.org/W2049391017","https://openalex.org/W2050890325","https://openalex.org/W2058839679","https://openalex.org/W2070744377","https://openalex.org/W2071467620","https://openalex.org/W2074451231","https://openalex.org/W2079578802","https://openalex.org/W2094668823","https://openalex.org/W2118920711","https://openalex.org/W2138571234","https://openalex.org/W2154018969","https://openalex.org/W2162693461","https://openalex.org/W2561843528","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3020087995","https://openalex.org/W2079040030","https://openalex.org/W2891194680","https://openalex.org/W2736737644","https://openalex.org/W2153062960","https://openalex.org/W2379187670","https://openalex.org/W2025296287","https://openalex.org/W2012772130","https://openalex.org/W2061262082","https://openalex.org/W2008628019"],"abstract_inverted_index":{"We":[0,62],"propose":[1],"a":[2,26],"new":[3],"sweeping":[4,53],"algorithm":[5],"which":[6],"discretizes":[7],"the":[8,12,22,48,64],"Legendre":[9,49],"transform":[10,50],"of":[11],"numerical":[13,23,71],"Hamiltonian":[14],"using":[15,29],"an":[16],"explicit":[17],"formula.":[18],"This":[19],"formula":[20],"yields":[21],"solution":[24],"at":[25],"grid":[27,34],"point":[28],"only":[30],"its":[31],"immediate":[32],"neighboring":[33],"values":[35],"and":[36,66,75],"is":[37,45],"easy":[38],"to":[39,47],"implement":[40],"numerically.":[41,61],"The":[42],"minimization":[43],"that":[44],"related":[46],"in":[51,73],"our":[52],"scheme":[54],"can":[55],"either":[56],"be":[57],"solved":[58],"analytically":[59],"or":[60],"illustrate":[63],"efficiency":[65],"accuracy":[67],"approach":[68],"with":[69],"several":[70],"examples":[72],"two":[74],"three":[76],"dimensions.":[77]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":7}],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}