English
Related papers

Related papers: High performance SIMD modular arithmetic for polyn…

200 papers

We present algorithms to perform modular polynomial multiplication or modular dot product efficiently in a single machine word. We pack polynomials into integers and perform several modular operations with machine integer or floating point…

Symbolic Computation · Computer Science 2013-06-19 Jean-Guillaume Dumas , Laurent Fousse , Bruno Salvy

We have repurposed Google Tensor Processing Units (TPUs), application-specific chips developed for machine learning, into large-scale dense linear algebra supercomputers. The TPUs' fast inter-core interconnects (ICI)s, physically…

Computational Physics · Physics 2022-09-14 Adam G. M. Lewis , Jackson Beall , Martin Ganahl , Markus Hauru , Shrestha Basu Mallick , Guifre Vidal

Computation of (approximate) polynomials common factors is an important problem in several fields of science, like control theory and signal processing. While the problem has been widely studied for scalar polynomials, the scientific…

Numerical Analysis · Mathematics 2021-06-02 A. Fazzi , N. Guglielmi , I. Markovsky

Analog in-memory computing (AIMC) cores offers significant performance and energy benefits for neural network inference with respect to digital logic (e.g., CPUs). AIMCs accelerate matrix-vector multiplications, which dominate these…

The problem is to evaluate a polynomial in several variables and its gradient at a power series truncated to some finite degree with multiple double precision arithmetic. To compensate for the cost overhead of multiple double precision and…

Mathematical Software · Computer Science 2021-03-16 Jan Verschelde

In this paper we propose a fast optimization algorithm for approximately minimizing convex quadratic functions over the intersection of affine and separable constraints (i.e., the Cartesian product of possibly nonconvex real sets). This…

Optimization and Control · Mathematics 2015-09-29 Reza Takapoui , Nicholas Moehle , Stephen Boyd , Alberto Bemporad

Matrix multiplications between asymmetric bit-width operands, especially between 8- and 4-bit operands are likely to become a fundamental kernel of many important workloads including neural networks and machine learning. While existing SIMD…

Machine Learning · Computer Science 2020-08-04 Dibakar Gope , Jesse Beu , Matthew Mattina

In current computer architectures, data movement (from die to network) is by far the most energy consuming part of an algorithm (10pJ/word on-die to 10,000pJ/word on the network). To increase memory locality at the hardware level and reduce…

Computational Physics · Physics 2018-01-17 H. Vincenti , R. Lehe , R. Sasanka , J-L. Vay

We consider the problem of evaluating distinct multivariate polynomials over several massive datasets in a distributed computing system with a single master node and multiple worker nodes. We focus on the general case when each multivariate…

Information Theory · Computer Science 2023-08-23 Wilton Kim , Stanislav Kruglik , Han Mao Kiah

In-memory computing (IMC) with single instruction multiple data (SIMD) setup enables memory to perform operations on the stored data in parallel to achieve high throughput and energy saving. To instruct a SIMD IMC hardware to compute a…

Emerging Technologies · Computer Science 2024-12-04 Xingyue Qian , Chenyang Lv , Zhezhi He , Weikang Qian

The problem of solving a system of polynomial equations is one of the most fundamental problems in applied mathematics. Among them, the problem of solving a system of binomial equations form a important subclass for which specialized…

Algebraic Geometry · Mathematics 2015-03-03 Tianran Chen , Dhagash Mehta

We provide a preliminary study on utilizing GPU (Graphics Processing Unit) to accelerate computation for three simulation optimization tasks with either first-order or second-order algorithms. Compared to the implementation using only CPU…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-04-19 Jinghai He , Haoyu Liu , Yuhang Wu , Zeyu Zheng , Tingyu Zhu

This paper presents a methodology for using LLVM-based tools to tune the DCA++ (dynamical clusterapproximation) application that targets the new ARM A64FX processor. The goal is to describethe changes required for the new architecture and…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-06-29 Joseph Huber , Weile Wei , Giorgis Georgakoudis , Johannes Doerfert , Oscar Hernandez

An alternating direction method of multipliers (ADMM) solver is described for optimal resource allocation problems with separable convex quadratic costs and constraints and linear coupling constraints. We describe a parallel implementation…

Optimization and Control · Mathematics 2019-07-09 Zawar Qureshi , Sebastian East , Mark Cannon

Specialized computational units that perform small matrix multiplications as primitive operations are typically present in modern AI accelerators. However, these Matrix Multiplication Units (MMUs) are often underutilized for many…

Data Structures and Algorithms · Computer Science 2025-09-25 Aleksandros Sobczyk , Giuseppe Sorrentino , Anastasios Zouzias

The singular value decomposition (SVD) is a powerful tool in modern numerical linear algebra, which underpins computational methods such as principal component analysis (PCA), low-rank approximations, and randomized algorithms. Many…

Mathematical Software · Computer Science 2026-04-10 Ahmad Abdelfattah , Massimiliano Fasi

Linear algebra operations have been widely used in big data analytics and scientific computations. Many works have been done on optimizing linear algebra operations on GPUs with regular-shaped input. However, few works focus on fully…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-02-19 Cody Rivera , Jieyang Chen , Nan Xiong , Shuaiwen Leon Song , Dingwen Tao

The paper presents the aspect of use of modern graphics accelerators supporting CUDA technology for high-performance computing in the field of linear algebra. Fully programmable graphic cards have been available for several years for both…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-06-27 Lukasz Swierczewski

This living paper reviews the present High Performance Computing (HPC) capabilities of the Tinker-HP molecular modeling package. We focus here on the reference, double precision, massively parallel molecular dynamics engine present in…

Mathematical Software · Computer Science 2024-01-11 Luc-Henri Jolly , Alejandro Duran , Louis Lagardère , Jay W. Ponder , Pengyu Ren , Jean-Philip Piquemal

Combinatorial optimization problems are computationally hard in general, but they are ubiquitous in our modern life. A coherent Ising machine (CIM) based on a multiple-pulse degenerate optical parametric oscillator (DOPO) is an alternative…