{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:29:58Z","timestamp":1787336998405,"version":"build-2736575974"},"reference-count":15,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>We present the details of a multiresolution method which we proposed at the Taormina Wavelet Conference in 1993 (see \"L-spline wavelets\" in Wavelets: Theory, Algorithms, and Applications, C. Chui, L. Montefusco, and L. Puccio, eds., Academic Press, New York, pp. 197--212) which is suitable for fitting functions or data on the sphere. The method is based on tensor products of polynomial splines and trigonometric splines and can be adapted to produce surfaces that are either tangent plane continuous or almost tangent plane continuous. The result is a convenient compression algorithm for dealing with large amounts of data on the sphere. We give full details of a computer implementation that is highly efficient with respect to both storage and computational cost. We also demonstrate the performance of the method on several test examples.<\/jats:p>","DOI":"10.1137\/s1064827598344388","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"724-746","source":"Crossref","is-referenced-by-count":65,"title":["A Multiresolution Tensor Spline Method for Fitting Functions on the Sphere"],"prefix":"10.1137","volume":"22","author":[{"given":"Tom","family":"Lyche","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Larry L.","family":"Schumaker","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","volume-title":"An introduction to wavelets through linear algebra","author":"Frazier Michael","year":"1999"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1080\/01630569508816605"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02243776"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02124735"},{"key":"R5","unstructured":"J. Goettelmann,\n                      Construction of Splines and Wavelets on the Sphere and Numerical Solutions to the Shallow Water Equations of Global Atmospheric Dynamics\n                      , dissertation, Johannes Gutenberg Univ., Mainz, Germany, 1998."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1145\/237748.237750"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"T. Lyche, K. M\u00f8rken, Spline\u2010wavelets of minimal support, Internat. Ser. Numer. Math., Vol. 105, Birkh\u00e4user, Basel, 1992, 177\u201319495c:41026","DOI":"10.1007\/978-3-0348-8619-2_10"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"Tom Lyche, Larry Schumaker, L\u2010spline wavelets, Wavelet Anal. Appl., Vol. 5, Academic Press, San Diego, CA, 1994, 197\u201321296c:42069","DOI":"10.1016\/B978-0-08-052084-1.50015-6"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1006\/jath.1998.3196"},{"key":"R10","unstructured":"Daniel Potts, Manfred Tasche, Interpolatory wavelets on the sphere, Ser. Approx. Decompos., Vol. 6, World Sci. Publishing, River Edge, NJ, 1995, 335\u201334298e:42040"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"P. Schr\u00f6der and W. Sweldens,\n                      Spherical wavelets: Efficiently representing functions on the sphere\n                      , in Computer Graphics Proceedings, Annual Conference Series, 1995, ACM SIGGRAPH, pp. 161\u2013172.","DOI":"10.1145\/218380.218439"},{"key":"R12","volume-title":"Spline functions: basic theory","author":"Schumaker Larry","year":"1993"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385718"},{"key":"R14","unstructured":"E. Stollnitz, T. D. DeRose, and D. Salesin,\n                      Wavelets for Computer Graphics\n                      , Morgan Kaufmann, San Francisco, 1996."},{"key":"R15","unstructured":"I. Weinreich,\n                      Biorthogonale Wavelets auf der Sph\u00e4re\n                      , dissertation, Tech. Univ. Aachen, Germany, 1997."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827598344388","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:40:05Z","timestamp":1787334005000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827598344388"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S1064827598344388"],"URL":"https:\/\/doi.org\/10.1137\/s1064827598344388","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}