Related papers: Fast algorithms for spherical harmonic expansions,…
The firefly algorithm has become an increasingly important tool of Swarm Intelligence that has been applied in almost all areas of optimization, as well as engineering practice. Many problems from various areas have been successfully solved…
This paper introduces a generalised 3rd-order Spectral Representation Method for the simulation of multi-dimensional stochastic fields with asymmetric non-linearities. The simulated random fields satisfy a prescribed Power Spectrum and…
This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and…
Recent work by McClarren & Hauck [29] suggests that the filtered spherical harmonics method represents an efficient, robust, and accurate method for radiation transport, at least in the two-dimensional (2D) case. We extend their work to the…
In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
We study the fundamental problem of butterfly (i.e. (2,2)-bicliques) counting in bipartite streaming graphs. Similar to triangles in unipartite graphs, enumerating butterflies is crucial in understanding the structure of bipartite graphs.…
In this paper, we show that extending the butterfly operations from the FFT algorithm to a general Butterfly Transform (BFT) can be beneficial in building an efficient block structure for CNN designs. Pointwise convolutions, which we refer…
Vector spherical harmonics on the unit sphere of $\mathbb{R}^3$ have broad applications in geophysics, quantum mechanics and astrophysics. In the representation of a tangent vector field, one needs to evaluate the expansion and the Fourier…
We propose fast, exact and efficient algorithms for the convolution of two arbitrary functions on the sphere which speed up computations by a factor \order{\sqrt{N}} compared to present methods where $N$ is the number of pixels. No…
This paper introduces the interpolative butterfly factorization for nearly optimal implementation of several transforms in harmonic analysis, when their explicit formulas satisfy certain analytic properties and the matrix representations of…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions…
Normalizing flows model complex probability distributions using maps obtained by composing invertible layers. Special linear layers such as masked and 1x1 convolutions play a key role in existing architectures because they increase…
For smooth finite fields $F_q$ (i.e., when $q-1$ factors into small primes) the Fast Fourier Transform (FFT) leads to the fastest known algebraic algorithms for many basic polynomial operations, such as multiplication, division,…
We investigate possibilities to speed up iterative algorithms for non-blind image deconvolution. We focus on algorithms in which convolution with the point-spread function to be deconvolved is used in each iteration, and aim at accelerating…
Firefly algorithm is a swarm based metaheuristic algorithm inspired by the flashing behavior of fireflies. It is an effective and an easy to implement algorithm. It has been tested on different problems from different disciplines and found…
This paper presents an adaptive randomized algorithm for computing the butterfly factorization of a $m\times n$ matrix with $m\approx n$ provided that both the matrix and its transpose can be rapidly applied to arbitrary vectors. The…
We propose a way of characterizing the algorithms computing a Walsh-Hadamard transform that consist of a sequence of arrays of butterflies ($I_{2^{n-1}}\otimes \text{DFT}_2$) interleaved by linear permutations. Linear permutations are those…
We present a unified treatment of the Fourier spectra of spherically symmetric nonlocal diffusion operators. We develop numerical and analytical results for the class of kernels with weak algebraic singularity as the distance between source…