{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T11:17:09Z","timestamp":1776683829936,"version":"3.51.2"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Methods Appl. Math."],"published-print":{"date-parts":[[2012]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We derive defect correction scheme for constructing the sequence of\n  polynomials of best approximation in the uniform norm to <jats:italic>1\/x<\/jats:italic> on a\n  finite interval with positive endpoints.  As an application, we\n  consider two-level methods for scalar elliptic partial differential\n  equation (PDE), where the relaxation on the fine grid uses the\n  aforementioned polynomial of best approximation. Based on a new\n  smoothing property of this polynomial smoother that we prove,\n  combined with a proper choice of the coarse space, we obtain as a\n  corollary, that the convergence rate of the resulting two-level\n  method is uniform with respect to the mesh parameters, coarsening\n  ratio and PDE coefficient variation.<\/jats:p>","DOI":"10.2478\/cmam-2012-0026","type":"journal-article","created":{"date-parts":[[2013,2,13]],"date-time":"2013-02-13T12:23:49Z","timestamp":1360758229000},"page":"448-468","source":"Crossref","is-referenced-by-count":21,"title":["Polynomial of Best Uniform Approximation to and Smoothing in Two-level Methods"],"prefix":"10.2478","volume":"12","author":[{"given":"Johannes","family":"Kraus","sequence":"first","affiliation":[{"name":"1Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences Altenberger Str. 69, 4040 Linz, Austria."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Panayot","family":"Vassilevski","sequence":"additional","affiliation":[{"name":"2Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P.O. Box 808, L-560, Livermore, CA 94551, U.S.A."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ludmil","family":"Zikatanov","sequence":"additional","affiliation":[{"name":"3Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/12\/4\/article-p448.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2012-0026\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:22:30Z","timestamp":1619101350000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/12\/4\/article-p448.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"references-count":0,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2012-0026","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012]]}}}