{"id":"https://openalex.org/W4388464750","doi":"https://doi.org/10.1137/22m1470463","title":"The Reflection Method for the Numerical Solution of Linear Systems","display_name":"The Reflection Method for the Numerical Solution of Linear Systems","publication_year":2023,"publication_date":"2023-11-01","ids":{"openalex":"https://openalex.org/W4388464750","doi":"https://doi.org/10.1137/22m1470463"},"language":"en","primary_location":{"id":"doi:10.1137/22m1470463","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1470463","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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/A5110129600","display_name":"Margherita Guida","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Margherita Guida","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5067652300","display_name":"Carlo Sbordone","orcid":"https://orcid.org/0000-0003-2297-153X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carlo Sbordone","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3254,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.88542351,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"65","issue":"4","first_page":"1137","last_page":"1151"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9958000183105469,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9944999814033508,"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/reflection","display_name":"Reflection (computer programming)","score":0.5965093374252319},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.48552966117858887},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44146206974983215},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40877383947372437},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3640051484107971},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24938440322875977}],"concepts":[{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.5965093374252319},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.48552966117858887},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44146206974983215},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40877383947372437},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3640051484107971},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24938440322875977},{"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:10.1137/22m1470463","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1470463","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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":9,"referenced_works":["https://openalex.org/W2000895477","https://openalex.org/W2005836623","https://openalex.org/W2009995718","https://openalex.org/W2025424390","https://openalex.org/W2054094260","https://openalex.org/W2073889532","https://openalex.org/W2076310535","https://openalex.org/W2963896572","https://openalex.org/W4301008583"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694"],"abstract_inverted_index":{"We":[0,45],"present":[1],"Cimmino's":[2],"reflection":[3],"algorithm":[4],"for":[5,49],"the":[6,26,32,38,42,50],"numerical":[7,87],"solution":[8],"of":[9,31,35,41],"linear":[10,76],"systems,":[11],"which":[12],"starts":[13],"with":[14,23,83,91],"an":[15,70],"arbitrary":[16],"point":[17,40],"in":[18],"$\\mathbb{R}^n$":[19],"that":[20],"gets":[21],"reflected":[22],"respect":[24],"to":[25,61,72],"system's":[27],"hyperplanes.":[28],"The":[29],"centroid":[30],"ensuing":[33],"collection":[34],"points":[36],"becomes":[37],"starting":[39],"next":[43],"iteration.":[44],"provide":[46],"error":[47],"estimates":[48],"convergence":[51],"at":[52],"each":[53],"step.":[54],"A":[55],"probabilistic":[56],"argument":[57],"is":[58,69],"also":[59,90],"devised":[60],"improve":[62],"this":[63],"elegant":[64],"geometrical":[65],"algorithm.":[66],"This":[67],"subject":[68],"opportunity":[71],"show":[73],"students":[74],"how":[75],"algebra":[77],"can":[78],"interact":[79],"fruitfully":[80],"not":[81],"only":[82],"algebra,":[84],"geometry,":[85],"and":[86,94],"analysis,":[88],"but":[89],"probability":[92],"theory":[93],"methods.":[95]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-25T09:21:30.201066","created_date":"2025-10-10T00:00:00"}