Fast spherical Fourier algorithms
Stefan Kunis,Daniel Potts +1 more
TLDR
This work improves well-known fast algorithms for the discrete spherical Fourier transform with a computational complexity of O(N2 log2 N), and presents, for the first time, a fast algorithm for scattered data on the sphere.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2003-12-01 and is currently open access. It has received 135 citations till now. The article focuses on the topics: Fast Fourier transform & Discrete Fourier transform (general).read more
Citations
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Journal ArticleDOI
A novel pole figure inversion method: specification of the MTEX algorithm
Ralf Hielscher,Helmut Schaeben +1 more
TL;DR: A novel algorithm for ODF (orientation density function) estimation from diffraction pole figures is presented which is especially well suited for sharp textures and high-resolution pole figures measured with respect to arbitrarily scattered specimen directions.
Journal ArticleDOI
Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms
TL;DR: This article provides a survey on the mathematical concepts behind the NFFT and its variants, as well as a general guideline for using the library.
Posted Content
Spherical CNNs
TL;DR: In this paper, the authors introduce the building blocks for constructing spherical CNNs and demonstrate the computational efficiency, numerical accuracy, and effectiveness of spherical convolutional networks applied to 3D model recognition and atomization energy regression.
Journal ArticleDOI
Fast Algorithms for Spherical Harmonic Expansions
Vladimir Rokhlin,Mark Tygert +1 more
TL;DR: An algorithm is introduced for the rapid evaluation at appropriately chosen nodes on the two-dimensional sphere of functions specified by their spherical harmonic expansions (known as the inverse spherical harmonic transform); the performance of the algorithm is illustrated via several numerical examples.
Proceedings Article
Gauge Equivariant Convolutional Networks and the Icosahedral CNN
TL;DR: In this paper, the authors extend the principle of equivariance to symmetry transformations to local gauge transformations, which enables the development of a very general class of convolutional neural networks on manifolds that depend only on the intrinsic geometry, including many popular methods from equivariant and geometric deep learning.
References
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Journal ArticleDOI
A fast algorithm for particle simulations
TL;DR: An algorithm is presented for the rapid evaluation of the potential and force fields in systems involving large numbers of particles whose interactions are Coulombic or gravitational in nature, making it considerably more practical for large-scale problems encountered in plasma physics, fluid dynamics, molecular dynamics, and celestial mechanics.
Journal ArticleDOI
Discrete Cosine Transform
TL;DR: In this article, a discrete cosine transform (DCT) is defined and an algorithm to compute it using the fast Fourier transform is developed, which can be used in the area of digital processing for the purposes of pattern recognition and Wiener filtering.
Reference BookDOI
Asymptotics and Special Functions
TL;DR: A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool as discussed by the authors, and it can be found in many libraries.
Book
Discrete Cosine Transform: Algorithms, Advantages, Applications
TL;DR: This paper presents two Dimensional DCT Algorithms and their relations to the Karhunen-Loeve Transform, and some applications of the DCT, which demonstrate the ability of these algorithms to solve the discrete cosine transform problem.