{"id":"https://openalex.org/W1987074755","doi":"https://doi.org/10.1137/050644203","title":"Schwarz Iterations for Symmetric Positive Semidefinite Problems","display_name":"Schwarz Iterations for Symmetric Positive Semidefinite Problems","publication_year":2006,"publication_date":"2006-12-26","ids":{"openalex":"https://openalex.org/W1987074755","doi":"https://doi.org/10.1137/050644203","mag":"1987074755"},"language":"en","primary_location":{"id":"doi:10.1137/050644203","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050644203","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5082240312","display_name":"Reinhard Nabben","orcid":"https://orcid.org/0000-0001-5076-9895"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Reinhard Nabben","raw_affiliation_strings":["Technical University of Berlin,"],"affiliations":[{"raw_affiliation_string":"Technical University of Berlin,","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047875137","display_name":"Daniel B. Szyld","orcid":"https://orcid.org/0000-0001-8010-0391"},"institutions":[{"id":"https://openalex.org/I84392919","display_name":"Temple University","ror":"https://ror.org/00kx1jb78","country_code":"US","type":"education","lineage":["https://openalex.org/I84392919"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel B. Szyld","raw_affiliation_strings":["[Temple University]"],"affiliations":[{"raw_affiliation_string":"[Temple University]","institution_ids":["https://openalex.org/I84392919"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082240312"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":null,"apc_paid":null,"fwci":4.7188,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.94969276,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"29","issue":"1","first_page":"98","last_page":"116"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9976000189781189,"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"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9968000054359436,"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/mathematics","display_name":"Mathematics","score":0.8893232345581055},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.8492358922958374},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.6119132041931152},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.5752054452896118},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.502633810043335},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49973011016845703},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4544858932495117},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.44757795333862305},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.44169795513153076},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38553574681282043},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37902703881263733},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.07782351970672607}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8893232345581055},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.8492358922958374},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.6119132041931152},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.5752054452896118},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.502633810043335},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49973011016845703},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4544858932495117},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.44757795333862305},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.44169795513153076},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38553574681282043},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37902703881263733},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07782351970672607},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050644203","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050644203","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.77.177","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.77.177","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.temple.edu/~szyld/papers/Szyld.Nabben.06.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":45,"referenced_works":["https://openalex.org/W105972517","https://openalex.org/W155934647","https://openalex.org/W1500921805","https://openalex.org/W1514324734","https://openalex.org/W1540854488","https://openalex.org/W1542243431","https://openalex.org/W1548589512","https://openalex.org/W1968647352","https://openalex.org/W1978286021","https://openalex.org/W1980500205","https://openalex.org/W1981310773","https://openalex.org/W1988048764","https://openalex.org/W1989435628","https://openalex.org/W1992381145","https://openalex.org/W1995124160","https://openalex.org/W2000290814","https://openalex.org/W2000582360","https://openalex.org/W2006401637","https://openalex.org/W2008808718","https://openalex.org/W2016499627","https://openalex.org/W2017085690","https://openalex.org/W2018834578","https://openalex.org/W2021257096","https://openalex.org/W2022925684","https://openalex.org/W2041257655","https://openalex.org/W2049707725","https://openalex.org/W2052114329","https://openalex.org/W2059356446","https://openalex.org/W2062246266","https://openalex.org/W2082732230","https://openalex.org/W2090963365","https://openalex.org/W2093184664","https://openalex.org/W2095749831","https://openalex.org/W2104126767","https://openalex.org/W2106990738","https://openalex.org/W2109044896","https://openalex.org/W2110275812","https://openalex.org/W2114226919","https://openalex.org/W2119862562","https://openalex.org/W2125231399","https://openalex.org/W2126036157","https://openalex.org/W2314343349","https://openalex.org/W2330756801","https://openalex.org/W2610857016","https://openalex.org/W3035235874"],"related_works":["https://openalex.org/W2023108949","https://openalex.org/W2093568309","https://openalex.org/W2091870430","https://openalex.org/W4297729421","https://openalex.org/W2022519819","https://openalex.org/W2963690976","https://openalex.org/W2014677830","https://openalex.org/W4205795567","https://openalex.org/W2013504776","https://openalex.org/W2016714604"],"abstract_inverted_index":{"Convergence":[0],"properties":[1],"of":[2,12,41],"additive":[3],"and":[4],"multiplicative":[5],"Schwarz":[6],"iterations":[7],"for":[8],"solving":[9],"linear":[10],"systems":[11],"equations":[13],"with":[14,49],"a":[15],"symmetric":[16],"positive":[17,34],"semidefinite":[18],"matrix":[19],"are":[20,31],"analyzed.":[21],"The":[22],"analysis":[23],"presented":[24],"applies":[25],"to":[26],"matrices":[27,37],"whose":[28],"principal":[29],"submatrices":[30],"nonsingular,":[32],"i.e.,":[33],"definite.":[35],"These":[36],"appear":[38],"in":[39],"discretizations":[40],"some":[42],"elliptic":[43],"partial":[44],"differential":[45],"equations,":[46],"e.g.,":[47],"those":[48],"Neumann":[50],"or":[51],"periodic":[52],"boundary":[53],"conditions.":[54]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
