Related papers: Fast Stencil Computations using Fast Fourier Trans…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…
Convolution models with long filters have demonstrated state-of-the-art reasoning abilities in many long-sequence tasks but lag behind the most optimized Transformers in wall-clock time. A major bottleneck is the Fast Fourier Transform…
Fast Fourier Transform (FFT) is an essential tool in scientific and engineering computation. The increasing demand for mixed-precision FFT has made it possible to utilize half-precision floating-point (FP16) arithmetic for faster speed and…
We propose an implementation of the algorithm for the fast Fourier transform (FFT) as a quantum circuit consisting of a combination of some quantum gates. In our implementation, a data sequence is expressed by a tensor product of vector…
This paper is devoted to the efficient numerical solution of the Helmholtz equation in a two- or three-dimensional rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and…
Constrained least squares problems arise in a variety of applications, and many iterative methods are already available to compute their solutions. This paper proposes a new efficient approach to solve nonnegative linear least squares…
Stencil computation is one of the most widely-used compute patterns in high performance computing applications. Spatial and temporal blocking have been proposed to overcome the memory-bound nature of this type of computation by moving…
Model-Based Iterative Reconstruction (MBIR) is important because direct methods, such as Filtered Back-Projection (FBP) can introduce significant noise and artifacts in sparse-angle tomography, especially for time-evolving samples. Although…
We present an efficient approach for writing architecture-agnostic parallel high-performance stencil computations in Julia, which is instantiated in the package ParallelStencil.jl. Powerful metaprogramming, costless abstractions and…
The bottleneck of micromagnetic simulations is the computation of the long-ranged magnetostatic fields. This can be tackled on regular N-node grids with Fast Fourier Transforms in time N logN, whereas the geometrically more versatile finite…
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…
Iterative solvers for large-scale linear systems such as Krylov subspace methods can diverge when the linear system is ill-conditioned, thus significantly reducing the applicability of these iterative methods in practice for…
We developed fast direct solver for 3D Helmholtz and Maxwell equations in layered medium. The algorithm is based on the ideas of cyclic reduction for separable matrices. For the grids with major uniform part (within the survey domain in the…
The Discrete Fourier Transform (DFT) underpins the solution to many inverse problems commonly possessing missing or un-measured frequency information. This incomplete coverage of Fourier space always produces systematic artefacts called…
The aim of this paper is to develop fast second-order accurate difference schemes for solving one- and two-dimensional time distributed-order and Riesz space fractional diffusion equations. We adopt the same measures for one- and…
Fast and accurate climate simulations and weather predictions are critical for understanding and preparing for the impact of climate change. Real-world weather and climate modeling consist of complex compound stencil kernels that do not…
One well adopted power grid simulation methodology is to factorize matrix once and perform only backward forward substitution with a deliberately chosen step size along the simulation. Since the required simulation time is usually long for…
In recent years there has been a renewed interest in finding fast algorithms to compute accurately the linear canonical transform (LCT) of a given function. This is driven by the large number of applications of the LCT in optics and signal…
A fast and accurate computational scheme for simulating nonlinear dynamic systems is presented. The scheme assumes that the system can be represented by a combination of components of only two different types: first-order low-pass filters…
Performing large-scale, accurate quantum simulations of many-fermion systems is a central challenge in quantum science, with applications in chemistry, materials, and high-energy physics. Despite significant progress, realizing generic…