caa a22 4500 46324690X CHVBK 20180405153328.0 cr unu---uuuuu 170326e20070801xx s 000 0 eng 10.1007/s00041-006-6915-y doi (NATIONALLICENCE)springer-10.1007/s00041-006-6915-y Efficient Reconstruction of Functions on the Sphere from Scattered Data [Elektronische Daten] [Jens Keiner, Stefan Kunis, Daniel Potts] Recently, fast and reliable algorithms for the evaluation of spherical harmonic expansions have been developed. The corresponding sampling problem is the computation of Fourier coefficients of a function from sampled values at scattered nodes. We consider a least squares approximation and an interpolation of the given data. Our main result is that the rate of convergence of the two proposed iterative schemes depends only on the mesh norm and the separation distance of the nodes. In conjunction with the nonequispaced FFT on the sphere, the reconstruction of N2 Fourier coefficients from M reasonably distributed samples is shown to take O(N2 log2 N + M) floating point operations. Numerical results support our theoretical findings. Birkhauser Boston, 2007 Keiner Jens Universität zu Lübeck, Institut für Mathematik, Wallstrasse 40, 23560 Lübeck, Germany aut Kunis Stefan Technische Universität Chemnitz, Fakultät für Mathematik, Reichenhainer Str. 39, 09107 Chemnitz, Germany aut Potts Daniel Technische Universität Chemnitz, Fakultät für Mathematik, Reichenhainer Str. 39, 09107 Chemnitz, Germany aut Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/4(2007-08-01), 435-458 1069-5869 13:4<435 2007 13 41 https://doi.org/10.1007/s00041-006-6915-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00041-006-6915-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Keiner Jens Universität zu Lübeck, Institut für Mathematik, Wallstrasse 40, 23560 Lübeck, Germany aut NATIONALLICENCE 700 1- Kunis Stefan Technische Universität Chemnitz, Fakultät für Mathematik, Reichenhainer Str. 39, 09107 Chemnitz, Germany aut NATIONALLICENCE 700 1- Potts Daniel Technische Universität Chemnitz, Fakultät für Mathematik, Reichenhainer Str. 39, 09107 Chemnitz, Germany aut NATIONALLICENCE 773 0- Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/4(2007-08-01), 435-458 1069-5869 13:4<435 2007 13 41 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer