{"id":"https://openalex.org/W2060675257","doi":"https://doi.org/10.1137/s1064827500380623","title":"Robust Parallel Smoothing for Multigrid Via Sparse Approximate Inverses","display_name":"Robust Parallel Smoothing for Multigrid Via Sparse Approximate Inverses","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2060675257","doi":"https://doi.org/10.1137/s1064827500380623","mag":"2060675257"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827500380623","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827500380623","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5063485610","display_name":"Oliver Br\u00f6ker","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Oliver Br\u00f6ker","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040323736","display_name":"Marcus J. Grote","orcid":"https://orcid.org/0000-0001-8129-0799"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marcus J. Grote","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109363970","display_name":"Carsten Mayer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carsten Mayer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109253345","display_name":"Arnold Reusken","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arnold Reusken","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":4.546,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.9449377,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"23","issue":"4","first_page":"1396","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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987999796867371,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9943000078201294,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.7779308557510376},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5875685214996338},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5250805616378784},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.4788375198841095},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4436682164669037},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.434966117143631},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3491557836532593},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3421388864517212},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1209355890750885},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.09077373147010803}],"concepts":[{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.7779308557510376},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5875685214996338},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5250805616378784},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.4788375198841095},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4436682164669037},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.434966117143631},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3491557836532593},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3421388864517212},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1209355890750885},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.09077373147010803},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/s1064827500380623","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827500380623","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.23.2462","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.23.2462","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.igpm.rwth-aachen.de/pub/reusken/SPAI_paper.ps.Z","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.26.4682","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.26.4682","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.inf.ethz.ch/pub/publications/tech-reports/3xx/358.ps.gz","raw_type":"text"},{"id":"pmh:oai:publications.rwth-aachen.de:163546","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/record/163546","pdf_url":null,"source":{"id":"https://openalex.org/S4306401362","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM journal on scientific computing 23(4), 1396-1417 (2001). doi:10.1137/S1064827500380623","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:publications.rwth-aachen.de:96215","is_oa":false,"landing_page_url":"http://publications.rwth-aachen.de/record/96215","pdf_url":null,"source":{"id":"https://openalex.org/S4306401362","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Z\u00fcrich : ETH, Seminar f\u00fcr Angewandte Mathematik, Research Report / Eidgen\u00f6ssische Technische Hochschule Z\u00fcrich, Seminar f\u00fcr Angewandte Mathematik 2000-13, 22 S. : graph. Darst. (2000).","raw_type":"info:eu-repo/semantics/book"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W194487525","https://openalex.org/W219299716","https://openalex.org/W1572639095","https://openalex.org/W1984797906","https://openalex.org/W1987832651","https://openalex.org/W1994805693","https://openalex.org/W1995214178","https://openalex.org/W1997831216","https://openalex.org/W2026502086","https://openalex.org/W2029490435","https://openalex.org/W2033340616","https://openalex.org/W2038516134","https://openalex.org/W2058273413","https://openalex.org/W2078114848","https://openalex.org/W2078311192","https://openalex.org/W2087851492","https://openalex.org/W2089099677","https://openalex.org/W2102369828","https://openalex.org/W2112968403","https://openalex.org/W2126036157","https://openalex.org/W2127981460","https://openalex.org/W2142304406","https://openalex.org/W2143408365","https://openalex.org/W2151317657","https://openalex.org/W2156588317","https://openalex.org/W2156736893","https://openalex.org/W2498157954","https://openalex.org/W2798909945","https://openalex.org/W3185776723","https://openalex.org/W4230055019"],"related_works":["https://openalex.org/W2077078424","https://openalex.org/W2182328658","https://openalex.org/W1519938374","https://openalex.org/W84272617","https://openalex.org/W613282331","https://openalex.org/W2092341060","https://openalex.org/W2625595466","https://openalex.org/W4205238550","https://openalex.org/W2001911974","https://openalex.org/W2102602799"],"abstract_inverted_index":{"Sparse":[0],"approximate":[1,32],"inverses":[2],"are":[3,10,64,157],"considered":[4],"as":[5],"smoothers":[6,60,63,156],"for":[7,92,167],"multigrid.":[8],"They":[9],"based":[11,78],"on":[12,79],"the":[13,44,89,111,114,135,138,141,151,160,174],"SPAI-Algorithm":[14],"[M.":[15],"J.":[16,22],"Grote":[17],"and":[18,70,137,154],"T.":[19],"Huckle,":[20],"SIAM":[21],"Sci.":[23],"Comput.,":[24],"18":[25],"(1997),":[26],"pp.":[27],"838--853],which":[28],"constructs":[29],"a":[30,36,49,80,164],"sparse":[31],"inverse":[33],"M":[34,118],"of":[35,52,58,117,121,130,140,176],"matrix":[37,82],"A":[38],"by":[39],"minimizing":[40],"I":[41],"-MA":[42],"in":[43],"Frobenius":[45],"norm.":[46],"This":[47],"yields":[48],"new":[50],"hierarchy":[51],"smoothers:":[53],"SPAI-0,":[54,76],"SPAI-1,":[55],"SPAI$(\\varepsilon)$.":[56],"Advantages":[57],"SPAI":[59,177],"over":[61],"classical":[62],"inherent":[65],"parallelism,":[66],"possible":[67],"local":[68],"adaptivity,":[69],"improved":[71],"robustness.":[72],"The":[73],"simplest":[74],"smoother,":[75],"is":[77,85,103,119,125],"diagonal":[81],"M.":[83],"It":[84],"shown":[86],"to":[87,106,128],"satisfy":[88],"smoothing":[90,102],"property":[91],"symmetric":[93],"positive":[94],"definite":[95],"problems.":[96],"Numerical":[97,171],"experiments":[98],"show":[99],"that":[100,120,129],"SPAI-0":[101,153],"usually":[104],"preferable":[105],"damped":[107],"Jacobi":[108],"smoothing.":[109,178],"For":[110],"SPAI-1":[112,155],"smoother":[113,142,162],"sparsity":[115],"pattern":[116],"A;":[122],"its":[123],"performance":[124],"typically":[126],"comparable":[127],"Gauss--Seidel":[131],"smoothing;":[132],"however,":[133],"both":[134],"computation":[136],"application":[139],"remain":[143],"inherently":[144],"parallel.":[145],"In":[146],"more":[147],"difficult":[148],"situations,":[149],"where":[150,169],"simpler":[152],"not":[158],"adequate,":[159],"SPAI$(\\varepsilon)$":[161],"provides":[163],"natural":[165],"procedure":[166],"improvement":[168],"needed.":[170],"examples":[172],"illustrate":[173],"usefulness":[175]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
