{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T04:25:06Z","timestamp":1765772706763},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2014,5,31]],"date-time":"2014-05-31T00:00:00Z","timestamp":1401494400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2015,2]]},"DOI":"10.1007\/s10444-014-9354-3","type":"journal-article","created":{"date-parts":[[2014,5,30]],"date-time":"2014-05-30T00:08:35Z","timestamp":1401408515000},"page":"191-230","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Fast memory efficient evaluation of spherical polynomials at scattered points"],"prefix":"10.1007","volume":"41","author":[{"given":"Kamen","family":"Ivanov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pencho","family":"Petrushev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,5,31]]},"reference":[{"key":"9354_CR1","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/BF01386223","volume":"2","author":"CW Clenshaw","year":"1960","unstructured":"Clenshaw, C. W., Curtis, A. R.: A method for numerical integration on an automatic computer. Numer. Math. 2, 197\u2013205 (1960)","journal-title":"Numer. Math."},{"key":"9354_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02888-9","volume-title":"Constructive approximation","author":"R DeVore","year":"1993","unstructured":"DeVore, R., Lorentz, J.: Constructive approximation. Springer, Berlin (1993)"},{"key":"9354_CR3","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1006\/aama.1994.1008","volume":"15","author":"JR Driscoll","year":"1994","unstructured":"Driscoll, J. R., Healy, D. M.: Computing fourier transforms and convolutions on the 2-sphere. Adv. Appl. Math. 15, 202\u2013250 (1994)","journal-title":"Adv. Appl. Math."},{"key":"9354_CR4","doi-asserted-by":"crossref","first-page":"1368","DOI":"10.1137\/0914081","volume":"14","author":"A Dutt","year":"1993","unstructured":"Dutt, A., Rokhlin, V.: Fast Fourier transforms for nonequispaced data. SIAM J. Sci. Stat. Comput. 14, 1368\u20131393 (1993)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"9354_CR5","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1137\/S0036141092236863","volume":"25","author":"T Erdelyi","year":"1994","unstructured":"Erdelyi, T., Magnus, A., Nevai, P.: Generalized Jacobi weights, christoffel functions, and Jacobi polynomials. SIAM J. Math. Anal. 25, 602\u2013614 (1994)","journal-title":"SIAM J. Math. Anal."},{"key":"9354_CR6","volume-title":"Higher Transcendental Functions, vol. 2","author":"A Erd\u00e9lyi","year":"1953","unstructured":"Erd\u00e9lyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Higher Transcendental Functions, vol. 2. McGraw-Hill, New York (1953)"},{"key":"9354_CR7","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1090\/S0002-9904-1933-05677-X","volume":"39","author":"L Fej\u00e9r","year":"1933","unstructured":"Fej\u00e9r, L.: On the infinite sequences arising in the theories of harmonic analysis, of interpolation, and of mechanical quadratures. Bull. Amer. Math. Soc. 39, 521\u2013534 (1933)","journal-title":"Bull. Amer. Math. Soc."},{"key":"9354_CR8","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/BF01474575","volume":"37","author":"L Fej\u00e9r","year":"1933","unstructured":"Fej\u00e9r, L.: Mechanische quadraturen mit positiven cotesschen zahlen. Math. Z. 37, 287\u2013309 (1933)","journal-title":"Math. Z."},{"key":"9354_CR9","doi-asserted-by":"crossref","first-page":"5621","DOI":"10.1016\/j.jcp.2009.05.014","volume":"228","author":"Z Gimbutas","year":"2009","unstructured":"Gimbutas, Z., Greengard, L.: A fast and stable method for rotating spherical harmonic expansions. J. Comput. Phys. 228, 5621\u20135627 (2009)","journal-title":"J. Comput. Phys."},{"key":"9354_CR10","doi-asserted-by":"crossref","first-page":"1420","DOI":"10.1137\/06067016X","volume":"29","author":"A Glaser","year":"2007","unstructured":"Glaser, A., Liu, X., Rokhlin, V.: A fast algorithm for the calculation of the roots of special functions. SIAM J. Scien. Comput. 29, 1420\u20131438 (2007)","journal-title":"SIAM J. Scien. Comput."},{"key":"9354_CR11","doi-asserted-by":"crossref","unstructured":"Ivanov, K.G., Petrushev, P.: Irregular sampling of band-limited functions on the sphere. Appl. Comput. Harmon. Anal. (2014), to appear","DOI":"10.1016\/j.acha.2014.05.001"},{"key":"9354_CR12","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1007\/s00209-008-0469-4","volume":"264","author":"KG Ivanov","year":"2010","unstructured":"Ivanov, K. G., Petrushev, P., Xu, Y.: Sub-exponentially localized kernels and frames induced by orthogonal expansions. Math. Z. 264, 361\u2013397 (2010)","journal-title":"Math. Z."},{"key":"9354_CR13","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1016\/j.jfa.2012.06.006","volume":"263","author":"KG Ivanov","year":"2012","unstructured":"Ivanov, K. G., Petrushev, P., Xu, Y.: Decomposition of spaces of distributions induced by tensor product bases. J. Funct. Anal. 263, 1147\u20131197 (2012)","journal-title":"J. Funct. Anal."},{"key":"9354_CR14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01891406","volume":"6","author":"KG Ivanov","year":"1989","unstructured":"Ivanov, K. G., Totik, V.: Fast decreasing polynomials. Constr. Approx. 6, 1\u201321 (1989)","journal-title":"Constr. Approx."},{"key":"9354_CR15","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/S0377-0427(03)00546-6","volume":"161","author":"S Kunis","year":"2003","unstructured":"Kunis, S., Potts, D.: Fast spherical fourier algorithms. J. Comput. Appl. Math. 161, 75\u201398 (2003)","journal-title":"J. Comput. Appl. Math."},{"key":"9354_CR16","doi-asserted-by":"crossref","unstructured":"Lai, M.-J., Schumaker, L.: Spline Functions on Triangulations. Cambridge University Press (2007)","DOI":"10.1017\/CBO9780511721588"},{"key":"9354_CR17","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/BF01261607","volume":"5","author":"M Mohlenkamp","year":"1999","unstructured":"Mohlenkamp, M.: A fast transform for spherical harmonics. J. Fourier Anal. Appl. 5, 159\u2013184 (1999)","journal-title":"J. Fourier Anal. Appl."},{"key":"9354_CR18","unstructured":"Moritz, H., Hofmann-Wellenhof, B.: Physical geodesy. Springer (2006)"},{"key":"9354_CR19","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1137\/040614359","volume":"38","author":"FJ Narcowich","year":"2006","unstructured":"Narcowich, F. J., Petrushev, P., Ward, J. D.: Localized tight frames on spheres. SIAM J. Math. Anal. 38, 574\u2013594 (2006)","journal-title":"SIAM J. Math. Anal."},{"key":"9354_CR20","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1016\/j.jfa.2006.02.011","volume":"238","author":"FJ Narcowich","year":"2006","unstructured":"Narcowich, F. J., Petrushev, P., Ward, J. D.: Decomposition of besov and triebel-lizorkin spaces on the sphere. J. Funct. Anal. 238, 530\u2013564 (2006)","journal-title":"J. Funct. Anal."},{"key":"9354_CR21","doi-asserted-by":"crossref","unstructured":"Nevai, P.: Orthogonal polynomials. Mem. AMS 18 (1979)","DOI":"10.1090\/memo\/0213"},{"key":"9354_CR22","unstructured":"Pavlis, N. K., Holmes, S. A., Kenyon, S.C., Factor, J. K.: An earth gravitational model to degree 2160: EGM2008, presented at the 2008 general assembly of the european geosciences union. Vienna, April 13\u201318, (2008)"},{"issue":"094108","key":"9354_CR23","first-page":"1","volume":"131","author":"MG Reuter","year":"2009","unstructured":"Reuter, M. G., Ratner, M. A., Seideman, T.: A fast method for solving both the time-dependent schroedinger equation in angular coordinates and its associated \u2019m-mixing\u2019 problem. J.Chem.Phys. 131(094108), 1\u20136 (2009). doi: 10.1063\/1.3213436","journal-title":"J.Chem.Phys."},{"issue":"1\u20135","key":"9354_CR24","first-page":"1","volume":"199","author":"DS Seljebotn","year":"2012","unstructured":"Seljebotn, D. S.: Wavemoth \u2013 fast spherical harmonic transforms by butterfly matrix compression. Astrophys. J. Suppl. Ser. 199(1\u20135), 1\u201312 (2012). doi: 10.1088\/0067-0049\/199\/1\/5","journal-title":"Astrophys. J. Suppl. Ser."},{"key":"9354_CR25","volume-title":"Fourier analysis on Euclidean spaces","author":"E Stein","year":"1971","unstructured":"Stein, E., Weiss, G.: Fourier analysis on Euclidean spaces. Princeton University Press, NJ (1971)"},{"key":"9354_CR26","unstructured":"Szego\u030b, G.: Orthogonal Polynomials, Vol. 23. Providence 4th edition (1975)"},{"key":"9354_CR27","unstructured":"Trefethen, L. N., et al.: Chebfun version 4.2 the chebfun development team (2011). http:\/\/www.maths.ox.ac.uk\/chebfun\/"},{"key":"9354_CR28","doi-asserted-by":"crossref","first-page":"4260","DOI":"10.1016\/j.jcp.2007.12.019","volume":"227","author":"M Tygert","year":"2008","unstructured":"Tygert, M.: Fast algorithms for spherical harmonic expansions, II. J. Comput. Phys. 227, 4260\u20134279 (2008)","journal-title":"J. Comput. Phys."},{"key":"9354_CR29","doi-asserted-by":"crossref","first-page":"6181","DOI":"10.1016\/j.jcp.2010.05.004","volume":"229","author":"M Tygert","year":"2010","unstructured":"Tygert, M.: Fast algorithms for spherical harmonic expansions, III. J. Comput. Phys. 229, 6181\u20136192 (2010)","journal-title":"J. Comput. Phys."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-014-9354-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-014-9354-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-014-9354-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,11]],"date-time":"2019-08-11T04:03:37Z","timestamp":1565496217000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-014-9354-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5,31]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,2]]}},"alternative-id":["9354"],"URL":"https:\/\/doi.org\/10.1007\/s10444-014-9354-3","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5,31]]}}}