FFTs for the 2-sphere-improvements and variations
FFTs for the 2-sphere-improvements and variations
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DOI：
10.1007/s00041-003-0018-9
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发表时间：
2003-01-01
影响因子：
1.2
通讯作者：
Moore, S
中科院分区：
文献类型：
--
作者：
Healy, DM;Rockmore, DN;Moore, S
Driscoll 和 Healy [18] 的早期工作提出了一种有效的算法，用于计算 2 球面上带限函数的傅立叶变换。在本文中，我们提出了原始算法的重新表述和变化，从而大大改进了逆变换，并随后改进了此类函数的卷积算法。所有操作最多需要 O(N log(2) N) 次操作，其中 N 是样本点的数量。我们还解决了实现方面的考虑因素，并给出了启发式方法，允许我们在 DEC、HP SGI mid Linux Pentium 平台上的 C 实现中进行可靠且计算高效的浮点实验。这些结果表明，该算法的变体对于大范围的有用问题规模来说既可靠又有效。性能似乎依赖于体系结构。本文最后简要讨论了一些潜在的应用。
Earlier work by Driscoll and Healy [18] has produced an efficient algorithm for computing the Fourier transform of band-limited functions on the 2-sphere. In this article we present a reformulation and variation of the original algorithm which results in a greatly improved inverse transform, and consequent improved convolution algorithm for such functions. All require at most O(N log(2) N) operations where N is the number of sample points. We also address implementation considerations and give heuristics tor allowing reliable and computationally efficient floating point experiments from our implementation in C on DEC, HP SGI mid Linux Pentium platforms. These results indicate that variations of the algorithm are both reliable and efficient for a large range of useful problem sizes. Performance appears to be architecture-dependent. The article concludes with a brief discussion of a few potential applications.