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The cornerstone of our approach is FFT-like algorithms, i.e., algorithms that scale almost linearly with respect to the sum of the dimension of the polynomial space and the number of evaluation points. These FFT-like algorithms allow us to compute one step of a descent method simultaneously for all starting points at almost the same cost as for one single starting point. The effectiveness of the proposed algorithms is demonstrated in various applications. In particular, we apply it to the Radon transform of a spherical function which allows us to detect lines in spherical patterns.<\/jats:p>","DOI":"10.1137\/130950070","type":"journal-article","created":{"date-parts":[[2015,3,19]],"date-time":"2015-03-19T14:48:17Z","timestamp":1426776497000},"page":"540-563","source":"Crossref","is-referenced-by-count":3,"title":["Fast Global Optimization on the Torus, the Sphere, and the Rotation Group"],"prefix":"10.1137","volume":"25","author":[{"given":"Manuel","family":"Gr\u00e4f","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ralf","family":"Hielscher","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,3,19]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.epsl.2008.04.020"},{"key":"atypb2","unstructured":"M. Abramowitz and I. A. 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