Related papers: cuPDLP-C: A Strengthened Implementation of cuPDLP …

We propose a generic algorithmic building block to accelerate training of machine learning models on heterogeneous compute systems. Our scheme allows to efficiently employ compute accelerators such as GPUs and FPGAs for the training of…

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…

GPUs have gained significant popularity over the past decade, extending beyond their original role in graphics rendering. This evolution has brought GPU security and reliability to the forefront of concerns. Prior research has shown that…

This paper presents, to the author's knowledge, the first graphics processing unit (GPU) accelerated program that solves the evolution of interacting scalar fields in an expanding universe. We present the implementation in NVIDIA's Compute…

Although the performance of commodity computers has improved drastically with the introduction of multicore processors and GPU computing, the standard R distribution is still based on single-threaded model of computation, using only a small…

Analysis of processing time and similarity of images generated between CPU and GPU architectures and sequential and parallel programming. For image processing a computer with AMD FX-8350 processor and an Nvidia GTX 960 Maxwell GPU was used,…

The Preconditioned Conjugate Gradient (PCG) method is widely used for solving linear systems of equations with sparse matrices. A recent version of PCG, Pipelined PCG, eliminates the dependencies in the computations of the PCG algorithm so…

Graphics processing units (GPU) had evolved from a specialized hardware capable to render high quality graphics in games to a commodity hardware for effective processing blocks of data in a parallel schema. This evolution is particularly…

Dynamic languages have become popular for scientific computing. They are generally considered highly productive, but lacking in performance. This paper presents Julia, a new dynamic language for technical computing, designed for performance…

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

In this paper we provide a detailed analysis of the iteration complexity of dual first order methods for solving conic convex problems. When it is difficult to project on the primal feasible set described by convex constraints, we use the…

Recent leaps in large language models (LLMs) caused a revolution in programming tools (like GitHub Copilot) that can help with code generation, debugging, and even performance optimization. In this paper, we focus on the capabilities of the…

The linear primal-dual hybrid gradient (PDHG) method is a first-order method that splits convex optimization problems with saddle-point structure into smaller subproblems. Unlike those obtained in most splitting methods, these subproblems…

The rapid growth of deep learning has driven exponential increases in model parameters and computational demands. NVIDIA GPUs and their CUDA-based software ecosystem provide robust support for parallel computing, significantly alleviating…

Principal component analysis (PCA) is a key statistical technique for multivariate data analysis. For large data sets the common approach to PCA computation is based on the standard NIPALS-PCA algorithm, which unfortunately suffers from…

Traditionally, there are several polynomial algorithms for linear programming including the ellipsoid method, the interior point method and other variants. Recently, Chubanov [Chubanov, 2015] proposed a projection and rescaling algorithm,…

Although large language models (LLMs) have achieved revolutionary breakthroughs in many fields, their large model size and high computational cost pose significant challenges for practical deployment on resource-constrained edge devices. To…

Large language models (LLMs) are computationally intensive. The computation workload and the memory footprint grow quadratically with the dimension (layer width). Most of LLMs' parameters come from the linear layers of the transformer…

Block Coordinate Update (BCU) methods enjoy low per-update computational complexity because every time only one or a few block variables would need to be updated among possibly a large number of blocks. They are also easily parallelized and…

It is now a noticeable trend in High Performance Computing that the systems are becoming more and more heterogeneous. Compute nodes with a host CPU are being equipped with accelerators, the latter being a GPU or FPGA cards or both. In many…