{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T11:42:20Z","timestamp":1648813340384},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[1994,6,1]],"date-time":"1994-06-01T00:00:00Z","timestamp":770428800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computing"],"published-print":{"date-parts":[[1994,6]]},"DOI":"10.1007\/bf02252987","type":"journal-article","created":{"date-parts":[[2005,11,22]],"date-time":"2005-11-22T14:30:38Z","timestamp":1132669838000},"page":"155-171","source":"Crossref","is-referenced-by-count":2,"title":["On the robustness of the dampedV-cycle of the wavelet frequency decomposition multigrid method"],"prefix":"10.1007","volume":"53","author":[{"given":"A.","family":"Rieder","sequence":"first","affiliation":[]},{"given":"X.","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"BF02252987_CR1","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/BF01462238","volume":"52","author":"R. E. Bank","year":"1988","unstructured":"Bank, R. E., Dupont, T.F., Yserentant, H.: The hierarchical basis multigrid method. Numer. Math.52, 427\u2013458 (1988).","journal-title":"Numer. Math."},{"key":"BF02252987_CR2","doi-asserted-by":"crossref","first-page":"1716","DOI":"10.1137\/0729097","volume":"6","author":"G. Beylkin","year":"1992","unstructured":"Beylkin, G.: On the representation of operators in bases of compactly supported wavelets. SIAM J. Numer. Anal.6, 1716\u20131740 (1992).","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02252987_CR3","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1090\/S0025-5718-1991-1090464-8","volume":"57","author":"J. H. Bramble","year":"1991","unstructured":"Bramble, J. H., Pasciak, J. E., Wang, J., Xu, J.: Convergence estimate for multigrid algorithms without regularity assumptions. Math. Comp.,57, 427\u2013458 (1991).","journal-title":"Math. Comp."},{"key":"BF02252987_CR4","volume-title":"The finite element methods for elliptic problems","author":"P. G. Ciarlet","year":"1987","unstructured":"Ciarlet, P. G.: The finite element methods for elliptic problems. New York: North-Holland 1987."},{"key":"BF02252987_CR5","first-page":"453","volume-title":"Wavelets and their applications","author":"R. R. Coifman","year":"1992","unstructured":"Coifman, R. R., Meyer, Y., Wickerhauser, M. V.: Size properties of wavelet packets. In: Ruskai (ed.) Wavelets and their applications, pp. 453\u2013470. Boston: Jones and Bartlett 1992."},{"key":"BF02252987_CR6","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1002\/cpa.3160410203","volume":"41","author":"I. Daubechies","year":"1988","unstructured":"Daubechies, I.: Orthonormal bases of compactly supporte wavelets. Comm. Pure Appl. Math.41, 906\u2013966 (1988).","journal-title":"Comm. Pure Appl. Math."},{"key":"BF02252987_CR7","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970104","volume-title":"Ten lectures on wavelets. CBMS-NSF Series in Applied Mathematics","author":"I. Daubechies","year":"1992","unstructured":"Daubechies, I.: Ten lectures on wavelets. CBMS-NSF Series in Applied Mathematics. Philadelphia: SIAM Publications 1992."},{"key":"BF02252987_CR8","volume-title":"Circulant matrices","author":"P. J. Davis","year":"1979","unstructured":"Davis, P. J.: Circulant matrices. New York: John Wiley 1979."},{"key":"BF02252987_CR9","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1137\/0523058","volume":"23","author":"T. Eirola","year":"1992","unstructured":"Eirola, T.: Sobolev characterization of solutions of dilation equations. SIAM J. Math. Anal.23, 1015\u20131030 (1992).","journal-title":"SIAM J. Math. Anal."},{"key":"BF02252987_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02427-0","volume-title":"Multi-grid methods and applications. Springer Series in Computational Mathematics","author":"W. Hackbusch","year":"1985","unstructured":"Hackbusch, W.: Multi-grid methods and applications. Springer Series in Computational Mathematics. New York: Springer 1985."},{"key":"BF02252987_CR11","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/BF01409786","volume":"56","author":"W. Hackbusch","year":"1989","unstructured":"Hackbusch, W.: The frequency decomposition multi-grid method, part I: Application to anisotropic equations. Numer. Math.56, 229\u2013245 (1989).","journal-title":"Numer. Math."},{"key":"BF02252987_CR12","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/BF01385869","volume":"63","author":"W. Hackbusch","year":"1992","unstructured":"Hackbusch, W.: The frequency decomposition multi-grid method, part II: Convergence analysis based on the additive Schwarz method. Numer. Math.63, 433\u2013453 (1992).","journal-title":"Numer. Math."},{"key":"BF02252987_CR13","unstructured":"Latto, A., Resnikoff, H. L., Tenenbaum, E.: The evaluation of connection coefficients of compactly supported wavelets. In: Proceedings of the USA-French Workshop on Wavelets and Turbulence. Princeton University 1991."},{"key":"BF02252987_CR14","first-page":"69","volume":"315","author":"S. Mallat","year":"1989","unstructured":"Mallat, S.: Multiresolution approximation and wavelet orthonormal bases ofL 2(R). Trans. Amer. Math. Soc.315, 69\u201387 (1989).","journal-title":"Trans. Amer. Math. Soc."},{"key":"BF02252987_CR15","volume-title":"Wavelets: algorithms and applications","author":"Y. Meyer","year":"1993","unstructured":"Meyer, Y.: Wavelets: algorithms and applications. Philadelphia: SIAM Publications 1993."},{"key":"BF02252987_CR16","unstructured":"Rieder, A., Wells, R. O., Jr., Zhou, X.: A wavelet approach to robust multilevel solvers for anisotropic elliptic problems. Technical Report 93-07, Rice University, 1993. Computational Mathematics Laboratory. Accepted for publication in Appl. Comput. Harmonic Anal. (ACHA)"},{"key":"BF02252987_CR17","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1137\/0729060","volume":"29","author":"J. Wang","year":"1992","unstructured":"Wang, J.: Convergence analysis without regularity assumptions for multigrid algorithms based on SOR smoothing. SIAM J. Numer. Anal.29, 987\u20131001 (1992).","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02252987_CR18","series-title":"Proceedings of NATO Advanced Research Workshop","volume-title":"Noncompact lie groups","author":"R. O. Wells Jr.","year":"1994","unstructured":"Wells, R. O., Jr., Zhou, X.: Wavelet interpolation and approximate solutions of elliptic partial differential equations. In: Wilson, R., Tanner, E. A. (eds.) Noncompact lie groups. Dordrecht: Kluwer, 1994. To appear. Proceedings of NATO Advanced Research Workshop."}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02252987.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02252987\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02252987","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T14:52:19Z","timestamp":1558018339000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02252987"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,6]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1994,6]]}},"alternative-id":["BF02252987"],"URL":"https:\/\/doi.org\/10.1007\/bf02252987","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,6]]}}}