{"id":"https://openalex.org/W1984480729","doi":"https://doi.org/10.1090/s0025-5718-08-02145-5","title":"A homographic best approximation problem with application to optimized Schwarz waveform relaxation","display_name":"A homographic best approximation problem with application to optimized Schwarz waveform relaxation","publication_year":2008,"publication_date":"2008-10-14","ids":{"openalex":"https://openalex.org/W1984480729","doi":"https://doi.org/10.1090/s0025-5718-08-02145-5","mag":"1984480729"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-08-02145-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02145-5","pdf_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02145-5/S0025-5718-08-02145-5.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02145-5/S0025-5718-08-02145-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003787991","display_name":"Daniel Bennequin","orcid":null},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"D. Bennequin","raw_affiliation_strings":["Institut de Math\u00c3\u00a9matiques de Jussieu, Universit\u00c3\u00a9 Paris VII, Case 7012, 2 place Jussieu, 75251 Paris Cedex 05, France","Institut de Math\u00e9matiques de Jussieu, Universit\u00e9 Paris VII, Case 7012, 2 place Jussieu, 75251 Paris Cedex 05, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00c3\u00a9matiques de Jussieu, Universit\u00c3\u00a9 Paris VII, Case 7012, 2 place Jussieu, 75251 Paris Cedex 05, France","institution_ids":["https://openalex.org/I3017942884","https://openalex.org/I204730241"]},{"raw_affiliation_string":"Institut de Math\u00e9matiques de Jussieu, Universit\u00e9 Paris VII, Case 7012, 2 place Jussieu, 75251 Paris Cedex 05, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I3017942884"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089456729","display_name":"Martin J. Gander","orcid":"https://orcid.org/0000-0001-8450-9223"},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"M. J. Gander","raw_affiliation_strings":["Section de Math\u00c3\u00a9matiques, Universit\u00c3\u00a9 de Gen\u00c3\u00a8ve, 2-4 rue du Li\u00c3\u00a8vre, CP 240, CH-1211 Gen\u00c3\u00a8ve, Switzerland","Section de Math\u00e9matiques, Universit\u00e9 de Gen\u00e8ve, 2-4 rue du Li\u00e8vre, CP 240, CH-1211 Gen\u00e8ve, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Section de Math\u00c3\u00a9matiques, Universit\u00c3\u00a9 de Gen\u00c3\u00a8ve, 2-4 rue du Li\u00c3\u00a8vre, CP 240, CH-1211 Gen\u00c3\u00a8ve, Switzerland","institution_ids":["https://openalex.org/I114457229"]},{"raw_affiliation_string":"Section de Math\u00e9matiques, Universit\u00e9 de Gen\u00e8ve, 2-4 rue du Li\u00e8vre, CP 240, CH-1211 Gen\u00e8ve, Switzerland","institution_ids":["https://openalex.org/I114457229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113857548","display_name":"Laurence Halpern","orcid":"https://orcid.org/0000-0002-7877-7130"},"institutions":[{"id":"https://openalex.org/I4210091279","display_name":"Universit\u00e9 Sorbonne Paris Nord","ror":"https://ror.org/0199hds37","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210091279"]},{"id":"https://openalex.org/I4210102686","display_name":"Laboratoire Analyse, G\u00e9om\u00e9trie et Applications","ror":"https://ror.org/018nzqy79","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210091279","https://openalex.org/I4210102686","https://openalex.org/I4210141950","https://openalex.org/I48825208"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"L. Halpern","raw_affiliation_strings":["LAGA,Institut Galil\u00c3\u00a9e, Universit\u00c3\u00a9 Paris XIII, 93430 Villetaneuse, France","LAGA, Institut Galil\u00e9e, Universit\u00e9 Paris XIII, 93430 Villetaneuse, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAGA,Institut Galil\u00c3\u00a9e, Universit\u00c3\u00a9 Paris XIII, 93430 Villetaneuse, France","institution_ids":["https://openalex.org/I4210102686","https://openalex.org/I4210091279"]},{"raw_affiliation_string":"LAGA, Institut Galil\u00e9e, Universit\u00e9 Paris XIII, 93430 Villetaneuse, France","institution_ids":["https://openalex.org/I4210102686","https://openalex.org/I4210091279"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5003787991"],"corresponding_institution_ids":["https://openalex.org/I204730241","https://openalex.org/I3017942884"],"apc_list":null,"apc_paid":null,"fwci":7.2627,"has_fulltext":true,"cited_by_count":124,"citation_normalized_percentile":{"value":0.97646776,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":100},"biblio":{"volume":"78","issue":"265","first_page":"185","last_page":"185"},"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":0.9988999962806702,"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":0.9988999962806702,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9918000102043152,"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":0.9901999831199646,"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/waveform","display_name":"Waveform","score":0.9183018207550049},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.7885607481002808},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6596916913986206},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.585261344909668},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5304479002952576},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5077184438705444},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44105812907218933},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43500056862831116},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2566223740577698},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.054693520069122314}],"concepts":[{"id":"https://openalex.org/C197424946","wikidata":"https://www.wikidata.org/wiki/Q1165717","display_name":"Waveform","level":3,"score":0.9183018207550049},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.7885607481002808},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6596916913986206},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.585261344909668},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5304479002952576},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5077184438705444},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44105812907218933},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43500056862831116},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2566223740577698},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.054693520069122314},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-08-02145-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02145-5","pdf_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02145-5/S0025-5718-08-02145-5.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:unige.ch:aou:unige:5445","is_oa":true,"landing_page_url":"https://archive-ouverte.unige.ch/unige:5445","pdf_url":null,"source":{"id":"https://openalex.org/S4306402259","display_name":"Archive ouverte UNIGE (University of Geneva)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114457229","host_organization_name":"University of Geneva","host_organization_lineage":["https://openalex.org/I114457229"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"ISSN: 0025-5718","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.140.6449","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.6449","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2009-78-265/S0025-5718-08-02145-5/S0025-5718-08-02145-5.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00111643v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00111643","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2006","raw_type":"Preprints, Working Papers, ..."}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-08-02145-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02145-5","pdf_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02145-5/S0025-5718-08-02145-5.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1984480729.pdf","grobid_xml":"https://content.openalex.org/works/W1984480729.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W355797926","https://openalex.org/W1480366635","https://openalex.org/W1482595527","https://openalex.org/W1503942291","https://openalex.org/W1535819777","https://openalex.org/W1572548753","https://openalex.org/W1589236075","https://openalex.org/W1594563152","https://openalex.org/W1594962983","https://openalex.org/W1965273420","https://openalex.org/W1975919514","https://openalex.org/W1987152170","https://openalex.org/W1998789711","https://openalex.org/W2007510482","https://openalex.org/W2008590430","https://openalex.org/W2009575526","https://openalex.org/W2012318642","https://openalex.org/W2020633626","https://openalex.org/W2025377524","https://openalex.org/W2031180106","https://openalex.org/W2033287169","https://openalex.org/W2046409434","https://openalex.org/W2068404638","https://openalex.org/W2078641415","https://openalex.org/W2092129801","https://openalex.org/W2099857391","https://openalex.org/W2119038858","https://openalex.org/W2144181355","https://openalex.org/W2171622994","https://openalex.org/W3143622134","https://openalex.org/W4285719527","https://openalex.org/W6600007727"],"related_works":["https://openalex.org/W1974895211","https://openalex.org/W2176409448","https://openalex.org/W2129841057","https://openalex.org/W3040712279","https://openalex.org/W2364769705","https://openalex.org/W4367555392","https://openalex.org/W2374664672","https://openalex.org/W2056136368","https://openalex.org/W2538520412","https://openalex.org/W2163370649"],"abstract_inverted_index":{"We":[0,43,89],"present":[1,44],"and":[2,55,66],"study":[3],"a":[4,80],"homographic":[5],"best":[6,35],"approximation":[7],"problem,":[8],"which":[9],"arises":[10],"in":[11,25,53],"the":[12,31,34,38,45,58,71,74],"analysis":[13,92],"of":[14,28,37,48,76,86],"waveform":[15,40,60],"relaxation":[16,41,61],"algorithms":[17,62],"with":[18,33,93],"optimized":[19],"transmission":[20,29,51],"conditions.":[21],"Its":[22],"solution":[23],"characterizes":[24],"each":[26],"class":[27,47],"conditions":[30,52],"one":[32],"performance":[36],"associated":[39],"algorithm.":[42],"particular":[46],"first":[49],"order":[50],"detail":[54],"show":[56],"that":[57],"new":[59],"are":[63],"well":[64],"posed":[65],"converge":[67],"much":[68],"faster":[69],"than":[70],"classical":[72],"one:":[73],"number":[75],"iterations":[77],"to":[78],"reach":[79],"certain":[81],"accuracy":[82],"can":[83],"be":[84],"orders":[85],"magnitudes":[87],"smaller.":[88],"illustrate":[90],"our":[91],"numerical":[94],"experiments.":[95]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":14},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":16},{"year":2012,"cited_by_count":6}],"updated_date":"2026-05-04T08:30:34.212998","created_date":"2025-10-10T00:00:00"}