Computing Fourier Transforms and Convolutions on the 2-Sphere
James R. Driscoll,D. M. Healy +1 more
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TLDR
Convolution theorems generalizing well known and useful results from the abelian case are used to develop a sampling theorem on the sphere, which reduces the calculation of Fourier transforms and convolutions of band-limited functions to discrete computations.About:
This article is published in Advances in Applied Mathematics.The article was published on 1994-06-01 and is currently open access. It has received 937 citations till now. The article focuses on the topics: Cyclotomic fast Fourier transform & Discrete Fourier transform (general).read more
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HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere
Krzysztof M. Gorski,Krzysztof M. Gorski,E. Hivon,A. J. Banday,Benjamin D. Wandelt,F. K. Hansen,Mstvos Reinecke,Matthia Bartelmann +7 more
TL;DR: This paper considers the requirements and implementation constraints on a framework that simultaneously enables an efficient discretization with associated hierarchical indexation and fast analysis/synthesis of functions defined on the sphere and demonstrates how these are explicitly satisfied by HEALPix.
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The Crust of the Moon as Seen by GRAIL
Mark A. Wieczorek,Gregory A. Neumann,Francis Nimmo,Walter S. Kiefer,G. Jeffrey Taylor,H. Jay Melosh,Roger J. Phillips,Sean C. Solomon,Sean C. Solomon,Jeffrey C. Andrews-Hanna,Sami W. Asmar,A. Konopliv,Frank G. Lemoine,David E. Smith,Michael M. Watkins,James G. Williams,Maria T. Zuber +16 more
TL;DR: In this article, high-resolution gravity data obtained from the dual Gravity Recovery and Interior Laboratory (GRAIL) spacecraft show that the bulk density of the Moon's highlands crust is 2550 kilograms per cubic meter, substantially lower than generally assumed.
Journal ArticleDOI
Characterization of anisotropy in high angular resolution diffusion-weighted MRI†
TL;DR: In this representation, it is shown that isotropic diffusion, anisotropic diffusion from a single fiber, and anisotrop diffusion from multiple fiber directions fall into distinct and separable channels and can be determined for any voxel without any prior information by a spherical harmonic transform.
Journal ArticleDOI
Analysis and design of spherical microphone arrays
TL;DR: Alternative spatial sampling schemes for the positioning of microphones on a sphere are presented, and the errors introduced by finite number of microphones, spatial aliasing, inaccuracies in microphone positioning, and measurement noise are investigated both theoretically and by using simulations.
The crust of the Moon as seen by GRAIL
Mark A. Wieczorek,Alexander S. Konopliv,Frank G. Lemoine,Erwan Mazarico,H. J. Melosh,Gregory A. Neumann,R. S. Park,Roger J. Phillips,David E. Smith,Sean C. Solomon,Maria T. Zuber +10 more
TL;DR: The Moon's gravity field shows that the lunar crust is less dense and more porous than was thought, and high-resolution gravity data obtained from the dual Gravity Recovery and Interior Laboratory (GRAIL) spacecraft show that the bulk density of the Moon's highlands crust is substantially lower than generally assumed.
References
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An algorithm for the machine calculation of complex Fourier series
J.W. Cooley,John W. Tukey +1 more
TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
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The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
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The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
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Introduction to Numerical Analysis
Josef Stoer,Roland Bulirsch +1 more
TL;DR: This well written book is enlarged by the following topics: B-splines and their computation, elimination methods for large sparse systems of linear equations, Lanczos algorithm for eigenvalue problems, implicit shift techniques for theLR and QR algorithm, implicit differential equations, differential algebraic systems, new methods for stiff differential equations and preconditioning techniques.