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Using the theory of the additive Schwarz methods, we will prove robustness of our method as a preconditioner applied to anisotropic equations.<\/p>","DOI":"10.1090\/s0025-5718-96-00740-5","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"983-997","source":"Crossref","is-referenced-by-count":3,"title":["The frequency decomposition multilevel method: A robust additive hierarchical basis preconditioner"],"prefix":"10.1090","volume":"65","author":[{"given":"Rob","family":"Stevenson","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"issue":"180","key":"1","doi-asserted-by":"publisher","first-page":"311","DOI":"10.2307\/2008314","article-title":"New convergence estimates for multigrid algorithms","volume":"49","author":"Bramble, James H.","year":"1987","journal-title":"Math. 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Stevenson, Robustness of the additive and multiplicative frequency decomposition multi-level method, Computing 54 (1995), 331\u2013346.","DOI":"10.1007\/BF02238231"},{"issue":"4","key":"12","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1137\/1034116","article-title":"Iterative methods by space decomposition and subspace correction","volume":"34","author":"Xu, Jinchao","year":"1992","journal-title":"SIAM Rev.","ISSN":"https:\/\/id.crossref.org\/issn\/1095-7200","issn-type":"print"},{"key":"13","isbn-type":"print","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1017\/S0962492900002385","article-title":"Old and new convergence proofs for multigrid methods","author":"Yserentant, Harry","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/0521443563"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1996-65-215\/S0025-5718-96-00740-5\/S0025-5718-96-00740-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-215\/S0025-5718-96-00740-5\/S0025-5718-96-00740-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:11:41Z","timestamp":1776719501000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-215\/S0025-5718-96-00740-5\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996]]},"references-count":13,"journal-issue":{"issue":"215","published-print":{"date-parts":[[1996,7]]}},"alternative-id":["S0025-5718-96-00740-5"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-96-00740-5","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[1996]]}}}