{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:27:49Z","timestamp":1787336869641,"version":"build-2736575974"},"reference-count":16,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>We generalize Harten's interpolatory multiresolution representation to include Hermite interpolation. Compact Hermite interpolation with optimal order accuracy is used in both the decomposition and reconstruction algorithm. The resulting multiple basis functions (biorthogonal multiwavelets) are symmetric or skew-symmetric, compact, and analytic. Harten's approach has several advantages: the multiresolution scheme is inherently discrete, nonperiodic boundary conditions are easy to implement, and the representation can be extended to nonuniform grids in bounded domains. We demonstrate the compression features of the new multiple basis functions by application to several examples.<\/jats:p>","DOI":"10.1137\/s1064827597315236","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1269-1317","source":"Crossref","is-referenced-by-count":16,"title":["Discrete Multiresolution Analysis Using Hermite Interpolation: Biorthogonal Multiwavelets"],"prefix":"10.1137","volume":"22","author":[{"given":"Robert F.","family":"Warming","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Richard M.","family":"Beam","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1006\/acha.1997.0211"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596311906"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0733047"},{"key":"R4","unstructured":"G. Dahlquist and \u00c5. Bj\u00f6rck,\n                      Numerical Methods\n                      , Prentice\u2010Hall, Englewood Cliffs, NJ, 1974."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01889598"},{"key":"R6","unstructured":"D. L. Donoho,\n                      Interpolating Wavelet Transforms\n                      , Technical Report 408, Department of Statistics, Stanford University, Stanford, CA, 1992."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(86)90077-6"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/0168-9274(93)90117-A"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"Ami Harten, Multiresolution representation and numerical algorithms: a brief review, ICASE\/LaRC Interdiscip. Ser. Sci. Eng., Vol. 4, Kluwer Acad. Publ., Dordrecht, 1997, 289\u20133221441582","DOI":"10.1007\/978-94-011-5412-3_11"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160481201"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/1031128"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1117\/12.172247"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"V. Strela, G. Strang, Finite element multiwavelets, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 454, Kluwer Acad. Publ., Dordrecht, 1995, 485\u201349696c:42072","DOI":"10.1007\/978-94-015-8577-4_33"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"W. Sweldens,\n                      The Lifting Scheme: A New Philosophy in Biorthogonal Wavelet Constructions\n                      , Proc. SPIE 2569, 1995, pp. 68\u201379.","DOI":"10.1117\/12.217619"},{"key":"R15","unstructured":"W. Sweldens and P Schroder,\n                      Building your own wavelets at home\n                      , in Wavelets in Computer Graphics, ACM SIGGRAPH Course Notes, 1966."},{"key":"R16","unstructured":"R. Warming and R. Beam,\n                      Discrete Multiresolution Analysis Using Hermite Interpolation: Biorthogonal Multiwavelets\n                      , NASA TM\u2010110434, 1997."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827597315236","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:34:19Z","timestamp":1787333659000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827597315236"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":16,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S1064827597315236"],"URL":"https:\/\/doi.org\/10.1137\/s1064827597315236","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}