Related papers: Fast algorithms for spherical harmonic expansions,…
The spherical harmonic transform is a powerful tool in the analysis of spherical data sets, such as the cosmic microwave background data. In this work, we present a new scheme for the spherical harmonic transforms that supports both CPU and…
We describe an algorithm for the application of the forward and inverse spherical harmonic transforms. It is based on a new method for rapidly computing the forward and inverse associated Legendre transforms by hierarchically applying the…
We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is…
The eigenfunctions of the Laplacian are a natural basis of functions for many tasks in computational mathematics. On the circle and sphere, the eigenfunctions are given by complex periodic exponentials and spherical harmonics, respectively,…
Recently, the butterfly approximation scheme and hierarchical approximations have been proposed for the efficient computation of integral transforms with oscillatory and with asymptotically smooth kernels. Combining both approaches, we…
A rapid transformation is derived between spherical harmonic expansions and their analogues in a bivariate Fourier series. The change of basis is described in two steps: firstly, expansions in normalized associated Legendre functions of all…
This paper is concerned with the fast computation of Fourier integral operators of the general form $\int_{\R^d} e^{2\pi\i \Phi(x,k)} f(k) d k$, where $k$ is a frequency variable, $\Phi(x,k)$ is a phase function obeying a standard…
We demonstrate a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions. In contrast to previous work, where spin transforms are computed independently, our algorithm permits the…
This paper presents an efficient multiscale butterfly algorithm for computing Fourier integral operators (FIOs) of the form $(\mathcal{L} f)(x) = \int_{R^d}a(x,\xi) e^{2\pi \i \Phi(x,\xi)}\hat{f}(\xi) d\xi$, where $\Phi(x,\xi)$ is a phase…
We discuss in some details a novel algorithm for performing partial-sky spherical harmonic transforms (SHT), building on the Fourier-sphere method of Reinecke et al (2023) handling efficiently high numbers of arbitrary locations on the…
In this paper, we report on very efficient algorithms for the spherical harmonic transform (SHT). Explicitly vectorized variations of the algorithm based on the Gauss-Legendre quadrature are discussed and implemented in the SHTns library…
We present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the…
The development of accurate and fast numerical schemes for the five fold Boltzmann collision integral represents a challenging problem in scientific computing. For a particular class of interactions, including the so-called hard spheres…
Spherical harmonics provide a smooth, orthogonal, and symmetry-adapted basis to expand functions on a sphere, and they are used routinely in physical and theoretical chemistry as well as in different fields of science and technology, from…
Butterflies are the smallest non-trivial subgraph in bipartite graphs, and therefore having efficient computations for analyzing them is crucial to improving the quality of certain applications on bipartite graphs. In this paper, we design…
The butterfly algorithm is a fast algorithm which approximately evaluates a discrete analogue of the integral transform \int K(x,y) g(y) dy at large numbers of target points when the kernel, K(x,y), is approximately low-rank when restricted…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
Many areas of science and engineering encounter data defined on spherical manifolds. Modelling and analysis of spherical data often necessitates spherical harmonic transforms, at high degrees, and increasingly requires efficient computation…
The graph Fourier transform (GFT) is an important tool for graph signal processing, with applications ranging from graph-based image processing to spectral clustering. However, unlike the discrete Fourier transform, the GFT typically does…
We present Wavemoth, an experimental open source code for computing scalar spherical harmonic transforms (SHTs). Such transforms are ubiquitous in astronomical data analysis. Our code performs substantially better than existing publicly…