{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:29:00Z","timestamp":1787329740292,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"name":"National Key Research and Development Program of China","award":["2016YFB0201304"],"award-info":[{"award-number":["2016YFB0201304"]}]},{"DOI":"10.13039\/501100002367","name":"Chinese Academy of Sciences","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002367","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["91430215"],"award-info":[{"award-number":["91430215"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["91530323"],"award-info":[{"award-number":["91530323"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>Various algebraic multigrid algorithms have been developed for solving problems in scientific and engineering computation over the past decades. They have been shown to be well-suited for solving discretized partial differential equations on unstructured girds in practice. One key ingredient of algebraic multigrid algorithms is a strategy for constructing an effective prolongation operator. Among many questions on constructing a prolongation, an important question is how to evaluate its quality. In this paper, we establish new characterizations (including sufficient condition, necessary condition, and equivalent condition) of the so-called ideal interpolation operator. Our result suggests that, compared with common wisdom, one has more room to construct an ideal interpolation, which can provide new insights for designing algebraic multigrid algorithms. Moreover, we derive a new expression for a class of ideal interpolation operators.<\/jats:p>","DOI":"10.1137\/17m1162779","type":"journal-article","created":{"date-parts":[[2018,6,20]],"date-time":"2018-06-20T14:17:31Z","timestamp":1529504251000},"page":"1693-1710","source":"Crossref","is-referenced-by-count":13,"title":["On the Ideal Interpolation Operator in Algebraic Multigrid Methods"],"prefix":"10.1137","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8374-6494","authenticated-orcid":true,"given":"Xuefeng","family":"Xu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chen-Song","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,6,20]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/0096-3003(86)90095-0"},{"key":"atypb2","volume-title":"Sparsity and Its Applications (Loughborough","author":"Brandt A.","year":"1983"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/17M1123456"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598344303"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1002\/nla.775"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/S106482750139892X"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598339402"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142903429742"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1002\/nla.437"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-28483-5"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2053"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599361047"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/060652312"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.4208\/nmtma.2015.w04si"},{"key":"atypb15","volume-title":"Multigrid Methods for Integral and Differential Equations (Bristol","author":"Ruge J.","year":"1983"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971057.ch4"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718003"},{"key":"atypb18","volume-title":"Multigrid","author":"Trottenberg U.","year":"2001"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/s211-001-8015-y"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/BF02238511"},{"key":"atypb21","volume-title":"Multilevel Block Factorization Preconditioners. 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Vassilevski,\n                      Lecture Notes on Multigrid Methods\n                      , Technical Report LLNL-TR-439511, Lawrence Livermore National Laboratory, Livermore, CA, 2010."},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1137\/1034116"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492917000083"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1162779","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:31:21Z","timestamp":1787326281000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1162779"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/17M1162779"],"URL":"https:\/\/doi.org\/10.1137\/17m1162779","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}