Related papers: Large-Scale Discrete Fourier Transform on TPUs

DFT is the numerical implementation of Fourier transform (FT), and it has many forms. Ordinary DFT (ODFT) and symmetric DFT (SDFT) are the two main forms of DFT. The most widely used DFT is ODFT, and the phase spectrum of this form is…

Density functional theory (DFT) remains the most widely used electronic structure method. Although exact in principle, in practice, it relies on approximations to the exchange-correlation (XC) functional, which is known to be a unique…

The increasing complexity and scale of photonic and electromagnetic devices demand efficient and accurate numerical solvers. In this work, we develop a parallel overlapping domain decomposition method (DDM) based on the finite-difference…

Tensor processing units (TPUs) are one of the most well-known machine learning (ML) accelerators utilized at large scale in data centers as well as in tiny ML applications. TPUs offer several improvements and advantages over conventional ML…

The advanced magnetic resonance (MR) image reconstructions such as the compressed sensing and subspace-based imaging are considered as large-scale, iterative, optimization problems. Given the large number of reconstructions required by the…

We propose a method to recover the sparse discrete Fourier transform (DFT) of a signal that is both noisy and potentially incomplete, with missing values. The problem is formulated as a penalized least-squares minimization based on the…

We present INQ, a new implementation of density functional theory (DFT) and time-dependent DFT (TDDFT) written from scratch to work on graphical processing units (GPUs). Besides GPU support, INQ makes use of modern code design features and…

Fluxonium qubits combine long coherence times with strong anharmonicity, making them a promising platform for scalable superconducting quantum processors. Recent experiments have demonstrated high-fidelity operations in multi-qubit…

Tucker decomposition is one of the most popular models for analyzing and compressing large-scale tensorial data. Existing Tucker decomposition algorithms usually rely on a single solver to compute the factor matrices and core tensor, and…

An existing hybrid MPI-OpenMP scheme is augmented with a CUDA-based fine grain parallelization approach for multidimensional distributed Fourier transforms, in a well-characterized pseudospectral fluid turbulence code. Basics of the hybrid…

Large deep learning models have demonstrated strong ability to solve many tasks across a wide range of applications. Those large models typically require training and inference to be distributed. Tensor parallelism is a common technique…

Large language model (LLM) inference increasingly depends on multi-GPU execution, yet existing inference parallelization strategies require layer-wise inter-rank synchronization, making end-to-end performance sensitive to workload…

Object orientation provides a flexible framework for the implementation of the convolution of arbitrary distributions of real-valued random variables. We discuss an algorithm which is based on the discrete Fourier transformation (DFT) and…

Nonlinear Fourier division Multiplexing (NFDM) can be realized from modulating the discrete nonlinear spectrum of an $N$-solitary waveform. To generate an $N$-solitary waveform from desired discrete spectrum (eigenvalue and discrete…

Quantum computers open up new avenues for modelling the physical properties of materials and molecules. Density Functional Theory (DFT) is the gold standard classical algorithm for predicting these properties, but relies on approximations…

The truncated Fourier transform (TFT) was introduced by van der Hoeven in 2004 as a means of smoothing the "jumps" in running time of the ordinary FFT algorithm that occur at power-of-two input sizes. However, the TFT still introduces these…

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…

A mathematical relation between elements of one- and multi-dimensional discrete Fourier transforms (DFT) is found. A method of analysing the multi-dimensional data by their single one-dimensional (1-D) DFT is offered. An experiment of…

We present an efficient real space formalism for hybrid exchange-correlation functionals in generalized Kohn-Sham density functional theory (DFT). In particular, we develop an efficient representation for any function of the real space…

Paper derives and analyzes a novel block Fast Fourier Transform (FFT) based joint detection algorithm. The paper compares the performance and complexity of the novel block-FFT based joint detector to that of the Cholesky based joint…