{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T02:08:24Z","timestamp":1740103704690,"version":"3.37.3"},"reference-count":12,"publisher":"Wiley","issue":"2-3","license":[{"start":{"date-parts":[[2010,3,3]],"date-time":"2010-03-03T00:00:00Z","timestamp":1267574400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"name":"US Department of Energy","award":["DE-FG02-03ER25574","DE-FC02-06ER25784"],"award-info":[{"award-number":["DE-FG02-03ER25574","DE-FC02-06ER25784"]}]},{"DOI":"10.13039\/100006227","name":"Lawrence Livermore National Laboratory","doi-asserted-by":"crossref","award":["B568677"],"award-info":[{"award-number":["B568677"]}],"id":[{"id":"10.13039\/100006227","id-type":"DOI","asserted-by":"crossref"}]},{"name":"National Science Foundation","award":["DMS-0749317","DMS-0811275"],"award-info":[{"award-number":["DMS-0749317","DMS-0811275"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2010,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Bootstrap algebraic multigrid (BAMG) is a multigrid\u2010based solver for matrix equations of the form <jats:italic>Ax<\/jats:italic>=<jats:italic>b<\/jats:italic>. Its aim is to automatically determine the interpolation weights used in algebraic multigrid (AMG) by locally fitting a set of test vectors that have been relaxed as solutions to the corresponding homogeneous equation, <jats:italic>Ax<\/jats:italic>=0, and are then possibly improved later using a multilevel eigensolver. This paper introduces a flexible variant of BAMG that determines the interpolation weights indirectly by \u2018collapsing\u2019 the unwanted connections in \u2018operator interpolation\u2019. Compared to BAMG, this <jats:italic>indirect<\/jats:italic> BAMG approach (<jats:italic>i<\/jats:italic>BAMG) is more in the spirit of classical AMG, which collapses unwanted connections in operator interpolation based on the (restrictive) assumption that smooth error is locally constant. This paper studies the numerical performance of <jats:italic>i<\/jats:italic>BAMG and establishes an equivalence, under certain assumptions, between it and a slightly modified (standard) BAMG scheme. To focus on camparing BAMG and <jats:italic>i<\/jats:italic>BAMG and exposing their behavior as the problem size grows, the numerical experiments concentrate on Poisson\u2010like scalar problems. Copyright \u00a9 2010 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/nla.711","type":"journal-article","created":{"date-parts":[[2010,3,3]],"date-time":"2010-03-03T09:04:01Z","timestamp":1267607041000},"page":"519-537","source":"Crossref","is-referenced-by-count":17,"title":["Operator\u2010based interpolation for bootstrap algebraic multigrid"],"prefix":"10.1002","volume":"17","author":[{"given":"T.","family":"Manteuffel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"McCormick","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Park","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Ruge","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,3,3]]},"reference":[{"volume-title":"Sparsity and Its Applications","year":"1984","author":"Brandt A","key":"e_1_2_1_2_2"},{"doi-asserted-by":"publisher","key":"e_1_2_1_3_2","DOI":"10.1137\/1.9780898719505"},{"doi-asserted-by":"publisher","key":"e_1_2_1_4_2","DOI":"10.1016\/0096-3003(86)90095-0"},{"volume-title":"Multigrid Methods","year":"1986","author":"Ruge J","key":"e_1_2_1_5_2"},{"key":"e_1_2_1_6_2","first-page":"1","volume-title":"Multiscale and Multiresolution Methods: Theory and Application","author":"Brandt A","year":"2001"},{"unstructured":"BrandtA BrannickJ KahlK livshitsI.A least squares based algebraic multigrid solver for Hermitian and positive definite systems.2009; Manuscript.","key":"e_1_2_1_7_2"},{"doi-asserted-by":"publisher","key":"e_1_2_1_8_2","DOI":"10.1137\/S1064827502418598"},{"doi-asserted-by":"publisher","key":"e_1_2_1_9_2","DOI":"10.1137\/050626272"},{"key":"e_1_2_1_10_2","first-page":"1","article-title":"Adaptive reduction\u2010based AMG","volume":"0","author":"MacLachlan S","year":"2005","journal-title":"Numerical Linear Algebra with Applications"},{"doi-asserted-by":"publisher","key":"e_1_2_1_11_2","DOI":"10.1137\/040614402"},{"key":"e_1_2_1_12_2","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1090\/S0025-5718-1977-0431719-X","article-title":"Multi\u2010level adaptive solutions to boundary value problems","volume":"31","author":"Brandt A","year":"1977","journal-title":"Mathematics of Computation"},{"key":"e_1_2_1_13_2","first-page":"1","article-title":"General highly accurate algebraic coarsening","volume":"10","author":"Brandt A","year":"2000","journal-title":"Electronic Transactions on Numerical Analysis"}],"container-title":["Numerical Linear Algebra with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnla.711","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnla.711","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.711","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T07:10:22Z","timestamp":1693465822000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/10.1002\/nla.711"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,3,3]]},"references-count":12,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2010,4]]}},"alternative-id":["10.1002\/nla.711"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1002\/nla.711","archive":["Portico"],"relation":{},"ISSN":["1070-5325","1099-1506"],"issn-type":[{"type":"print","value":"1070-5325"},{"type":"electronic","value":"1099-1506"}],"subject":[],"published":{"date-parts":[[2010,3,3]]}}}