{"id":"https://openalex.org/W2605147253","doi":"https://doi.org/10.1137/17m1123456","title":"Optimal Interpolation and Compatible Relaxation in Classical Algebraic Multigrid","display_name":"Optimal Interpolation and Compatible Relaxation in Classical Algebraic Multigrid","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2605147253","doi":"https://doi.org/10.1137/17m1123456","mag":"2605147253"},"language":"en","primary_location":{"id":"doi:10.1137/17m1123456","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1123456","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/A5074112892","display_name":"James Brannick","orcid":"https://orcid.org/0000-0003-1637-0439"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"James Brannick","raw_affiliation_strings":["Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019039666","display_name":"Fei Cao","orcid":"https://orcid.org/0000-0002-1367-8692"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fei Cao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088264517","display_name":"Karsten Kahl","orcid":"https://orcid.org/0000-0002-3510-3320"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Karsten Kahl","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057085539","display_name":"Robert D. Falgout","orcid":"https://orcid.org/0000-0003-4884-0087"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert D. Falgout","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029270343","display_name":"Xiaozhe Hu","orcid":"https://orcid.org/0000-0001-7533-0416"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaozhe Hu","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":2.3099,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.86417109,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"40","issue":"3","first_page":"A1473","last_page":"A1493"},"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":0.9997000098228455,"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":0.9997000098228455,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9941999912261963,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9865999817848206,"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/mathematics","display_name":"Mathematics","score":0.7886831760406494},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.7046635150909424},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.6067662835121155},{"id":"https://openalex.org/keywords/sparse-grid","display_name":"Sparse grid","score":0.5434515476226807},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5257374048233032},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5212367177009583},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5145346522331238},{"id":"https://openalex.org/keywords/nearest-neighbor-interpolation","display_name":"Nearest-neighbor interpolation","score":0.4690108001232147},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39532747864723206},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.34302982687950134},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3013347387313843},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1487460732460022},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1389768123626709},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.11908948421478271}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7886831760406494},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7046635150909424},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.6067662835121155},{"id":"https://openalex.org/C156439662","wikidata":"https://www.wikidata.org/wiki/Q7573793","display_name":"Sparse grid","level":2,"score":0.5434515476226807},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5257374048233032},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5212367177009583},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5145346522331238},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.4690108001232147},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39532747864723206},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.34302982687950134},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3013347387313843},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1487460732460022},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1389768123626709},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.11908948421478271},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1123456","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1123456","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1826690079","https://openalex.org/W1970627157","https://openalex.org/W1986746311","https://openalex.org/W1992935956","https://openalex.org/W2034374312","https://openalex.org/W2064878022","https://openalex.org/W2078687549","https://openalex.org/W2080753469","https://openalex.org/W2086079525","https://openalex.org/W2142304406","https://openalex.org/W2167128668","https://openalex.org/W2912759508","https://openalex.org/W2964264054"],"related_works":["https://openalex.org/W2216935333","https://openalex.org/W1991081991","https://openalex.org/W2377616530","https://openalex.org/W2161759000","https://openalex.org/W2347398662","https://openalex.org/W2079541091","https://openalex.org/W2129302469","https://openalex.org/W2347981043","https://openalex.org/W2382426030","https://openalex.org/W4303468906"],"abstract_inverted_index":{"In":[0,80],"this":[1],"paper,":[2],"we":[3,82],"consider":[4],"a":[5,25,31,54,63,77,84,92],"classical":[6],"algebraic":[7],"multigrid":[8],"(AMG)":[9],"form":[10],"of":[11,35,48,71],"optimal":[12,59,97],"interpolation":[13,28,60,98,110,126],"that":[14,29,61,90,103],"directly":[15],"minimizes":[16,30],"the":[17,36,46,49,68,72,96,104,119,123],"two-grid":[18,74,120],"convergence":[19,69],"rate":[20,70],"and":[21,52],"compare":[22],"it":[23],"with":[24,108,122,135],"so-called":[26],"ideal":[27,125],"weak":[32],"approximation":[33,94],"property":[34],"coarse":[37,50],"space.":[38],"We":[39,100],"study":[40],"compatible":[41],"relaxation":[42],"type":[43],"estimates":[44],"for":[45,76,130],"quality":[47],"grid":[51],"derive":[53],"new":[55],"sharp":[56],"measure":[57],"using":[58],"provides":[62],"guaranteed":[64],"lower":[65],"bound":[66],"on":[67],"resulting":[73],"method":[75,107,121],"given":[78],"grid.":[79],"addition,":[81],"design":[83],"generalized":[85],"bootstrap":[86,105],"AMG":[87,106],"setup":[88],"algorithm":[89],"computes":[91],"sparse":[93,109],"to":[95],"matrix.":[99],"demonstrate":[101],"numerically":[102],"matrix":[111],"(and":[112],"spanning":[113],"multiple":[114],"levels)":[115],"converges":[116],"faster":[117],"than":[118],"standard":[124],"(a":[127],"dense":[128],"matrix)":[129],"various":[131],"scalar":[132],"diffusion":[133,138],"problems":[134],"highly":[136],"varying":[137],"coefficient.":[139]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2}],"updated_date":"2026-07-17T09:13:05.818461","created_date":"2025-10-10T00:00:00"}
