{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T11:54:47Z","timestamp":1790942087261,"version":"4.1.0"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>Harten's framework is a nonlinear generalization of the wavelet framework. Previously, the choice of discretization (scaling function) in Harten multiresolution schemes has been limited to point-value, cell-average, and hat-based discretization. This paper shows how to construct multiresolution schemes consistent with Harten's framework for a variety of discretizations. The construction here begins with the discrete operators and deduces the corresponding continuous operators, reversing the order of the usual approach. This construction yields as a special case essentially nonoscillatory (ENO) multiresolution schemes for any order of spline discretization and also has the flexibility to define multiresolution schemes with nonspline discretizations. An error-control strategy is also developed.<\/jats:p>","DOI":"10.1137\/060663763","type":"journal-article","created":{"date-parts":[[2008,8,20]],"date-time":"2008-08-20T18:01:55Z","timestamp":1219255315000},"page":"2953-2977","source":"Crossref","is-referenced-by-count":12,"title":["ENO Multiresolution Schemes with General Discretizations"],"prefix":"10.1137","volume":"46","author":[{"given":"Pascal","family":"Getreuer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fran\u00e7ois G.","family":"Meyer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,8,20]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050252"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1006\/acha.2001.0356"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2006.12.003"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-004-0122-5"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019104118012"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596308822"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"T. Cecil, J. Qian, and S. Osher,\n                      Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions\n                      , J. Comput. Phys., 2003.","DOI":"10.1016\/j.jcp.2003.11.010"},{"key":"R8","unstructured":"R. Claypoole, G. Davis, W. Sweldens, and R. Baraniuk,\n                      Nonlinear wavelet transforms for image coding\n                      , in Proceedings of the 31st IEEE Asilomar Conference, Pacific Grove, CA, 1997."},{"key":"R9","unstructured":"A. Cohen and B. Mate\u00ef,\n                      Compact representation of images by edge adapted multiscale transforms\n                      , in Proceedings of the International Conference on Image Processing, Thessaloniki, Greece, IEEE, 2001."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/S1063-5203(03)00061-7"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"S. 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