{"id":"https://openalex.org/W3217695991","doi":"https://doi.org/10.1007/s11075-021-01234-2","title":"Discussions on a macro multi-time scales coupling method: existence and uniqueness of the numerical solution and strict non-negativity of the Schur complement","display_name":"Discussions on a macro multi-time scales coupling method: existence and uniqueness of the numerical solution and strict non-negativity of the Schur complement","publication_year":2021,"publication_date":"2021-11-26","ids":{"openalex":"https://openalex.org/W3217695991","doi":"https://doi.org/10.1007/s11075-021-01234-2","mag":"3217695991"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-021-01234-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-021-01234-2","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5039274693","display_name":"Eliass Zafati","orcid":"https://orcid.org/0000-0002-5927-6525"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Eliass Zafati","raw_affiliation_strings":["EDF R&D, ERMES, 7 Boulevard Gaspard Monge, 91120, Palaiseau, France"],"raw_orcid":"https://orcid.org/0000-0002-5927-6525","affiliations":[{"raw_affiliation_string":"EDF R&D, ERMES, 7 Boulevard Gaspard Monge, 91120, Palaiseau, France","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039274693"],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.1514,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.55193901,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"90","issue":"4","first_page":"1389","last_page":"1417"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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":0.9995999932289124,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9991999864578247,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9986000061035156,"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/schur-complement","display_name":"Schur complement","score":0.8529648184776306},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8069564700126648},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7849945425987244},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.7106035947799683},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6194177865982056},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.479166179895401},{"id":"https://openalex.org/keywords/negativity-effect","display_name":"Negativity effect","score":0.46829476952552795},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4622042179107666},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.4613931179046631},{"id":"https://openalex.org/keywords/macro","display_name":"Macro","score":0.42458418011665344},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37568455934524536},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3332037329673767},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10530677437782288},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08466842770576477},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06719836592674255},{"id":"https://openalex.org/keywords/social-psychology","display_name":"Social psychology","score":0.050243526697158813},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.0499664843082428}],"concepts":[{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.8529648184776306},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8069564700126648},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7849945425987244},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.7106035947799683},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6194177865982056},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.479166179895401},{"id":"https://openalex.org/C7453019","wikidata":"https://www.wikidata.org/wiki/Q16254302","display_name":"Negativity effect","level":2,"score":0.46829476952552795},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4622042179107666},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.4613931179046631},{"id":"https://openalex.org/C166955791","wikidata":"https://www.wikidata.org/wiki/Q629579","display_name":"Macro","level":2,"score":0.42458418011665344},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37568455934524536},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3332037329673767},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10530677437782288},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08466842770576477},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06719836592674255},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.050243526697158813},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0499664843082428},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-021-01234-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-021-01234-2","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W653474616","https://openalex.org/W1545114773","https://openalex.org/W1575147392","https://openalex.org/W1591608973","https://openalex.org/W1955908400","https://openalex.org/W1970056665","https://openalex.org/W1979157957","https://openalex.org/W1990023626","https://openalex.org/W2004285602","https://openalex.org/W2036230371","https://openalex.org/W2036958726","https://openalex.org/W2041067518","https://openalex.org/W2042183992","https://openalex.org/W2048355779","https://openalex.org/W2054731935","https://openalex.org/W2055417657","https://openalex.org/W2068995072","https://openalex.org/W2084948094","https://openalex.org/W2094383942","https://openalex.org/W2100166562","https://openalex.org/W2107083479","https://openalex.org/W2118786393","https://openalex.org/W2141870784","https://openalex.org/W2172037311","https://openalex.org/W2253406547","https://openalex.org/W2316564661","https://openalex.org/W2520204399","https://openalex.org/W2587288333","https://openalex.org/W2594332644","https://openalex.org/W2767215625","https://openalex.org/W2802235862","https://openalex.org/W2901742092","https://openalex.org/W4211006520","https://openalex.org/W4237872734","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2146459776","https://openalex.org/W1975201729","https://openalex.org/W2068155564","https://openalex.org/W1980119950","https://openalex.org/W3092306907","https://openalex.org/W2471027283","https://openalex.org/W2013908502","https://openalex.org/W1796128968","https://openalex.org/W2039023896","https://openalex.org/W2028790718"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}