{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:27:43Z","timestamp":1787333263805,"version":"build-2736575974"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>The full multigrid (FMG) algorithm is often claimed to achieve so-called discretization-level accuracy. In this paper, this notion is formalized by defining a worst-case relative accuracy measure, denoted $E_{FMG}^{\\ell}$, which compares the total error of the $\\ell$-level FMG solution against the inherent discretization error. This measure can be used for tuning algorithmic components so as to obtain discretization-level accuracy. A Fourier analysis is developed for estimating $E_{FMG}^{\\ell}$, and the resulting estimates are confirmed by numerical tests.<\/jats:p>","DOI":"10.1137\/100786101","type":"journal-article","created":{"date-parts":[[2010,10,12]],"date-time":"2010-10-12T19:07:47Z","timestamp":1286910467000},"page":"3108-3129","source":"Crossref","is-referenced-by-count":7,"title":["Accuracy Measures and Fourier Analysis for the Full Multigrid Algorithm"],"prefix":"10.1137","volume":"32","author":[{"given":"Carmen","family":"Rodrigo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francisco J.","family":"Gaspar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cornelis W.","family":"Oosterlee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Irad","family":"Yavneh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,10,12]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2005.12.023"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1977-0431719-X"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"A. Brandt,\n                      Guide to multigrid development\n                      , in Multigrid Methods Lectures Notes in Mathematics, vol. 960, W. Hackbusch and U. Trottenberg, eds., Springer, Berlin, 1982, pp. 220\u2013312.","DOI":"10.1007\/BFb0069930"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/0731087"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/080713483"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"W. Hackbusch,\n                      Multi\u2013grid Methods and Applications\n                      , Springer, Berlin, 1985.","DOI":"10.1007\/978-3-662-02427-0"},{"key":"R7","unstructured":"P. W. Hemker,\n                      Lecture Notes on Defect Correction\n                      , Technical Report Lecture Notes, Centrum voor Wiskunde en Informatica (CWI), Amsterdam, 2001."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1002\/nla.356"},{"key":"R9","first-page":"63","volume":"11","author":"Kronsj\u00f6 L.","year":"1971","journal-title":"BIT","ISSN":"https:\/\/id.crossref.org\/issn\/0006-3835","issn-type":"print"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01933003"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827501397950"},{"key":"R12","doi-asserted-by":"crossref","unstructured":"E. M. Stein,\n                      Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals\n                      , Princeton University Press, New Jersey, 1993.","DOI":"10.1515\/9781400883929"},{"key":"R13","unstructured":"R. Stevenson,\n                      On the Validity of Local Mode Analysis of Multi-grid Methods\n                      , Ph.D. thesis, Rijks Univ. Utrecht, The Netherlands, 1990."},{"key":"R14","doi-asserted-by":"crossref","unstructured":"K. St\u00fcben and U. Trottenberg,\n                      Multigrid methods: Fundamental algorithms, model problem analysis and applications\n                      , in Multigrid Methods, Lecture Notes in Math. 960, W. Hackbusch and U. Trottenberg, eds., Springer-Verlag, Berlin, 1982, pp. 1\u2013176.","DOI":"10.1007\/BFb0069928"},{"key":"R15","unstructured":"U. Trottenberg, C. W. Oosterlee, and A. Sch\u00fcller,\n                      Multigrid\n                      , Academic Press, New York, 2001."},{"key":"R16","unstructured":"P. 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Joppich,\n                      Practical Fourier Analysis for Multigrid Methods\n                      , Chapman and Hall\/CRC Press, Boca Raton, FL, 2005.","DOI":"10.1201\/9781420034998"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/100786101","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:45:55Z","timestamp":1787330755000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/100786101"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":18,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/100786101"],"URL":"https:\/\/doi.org\/10.1137\/100786101","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}