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For the parallel-in-time integration method Parareal, pipelining can be used to hide some of the cost of the serial correction step and improve its efficiency. The paper introduces a basic OpenMP implementation of pipelined Parareal and…

Mathematical Software · Computer Science 2019-11-12 Daniel Ruprecht

Graph construction from a given set of edges is a data-intensive operator that appears in social network analysis, ontology enabled databases, and, other analytics processing. The operator represents an edge list to compressed sparse row…

Databases · Computer Science 2012-11-01 Sandeep Gupta

To accelerate distributed training, many gradient compression methods have been proposed to alleviate the communication bottleneck in synchronous stochastic gradient descent (S-SGD), but their efficacy in real-world applications still…

Machine Learning · Computer Science 2023-06-16 Lin Zhang , Longteng Zhang , Shaohuai Shi , Xiaowen Chu , Bo Li

Due to its optimal complexity, the multigrid (MG) method is one of the most popular approaches for solving large-scale linear systems arising from the discretization of partial differential equations. However, the parallel implementation of…

Numerical Analysis · Mathematics 2025-02-27 Hardik Kothari , Maria Giuseppina Chiara Nestola , Marco Favino , Rolf Krause

The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…

Numerical Analysis · Mathematics 2021-08-31 Abal-Kassim Cheik Ahamed , Frédéric Magoulès

Coded computation techniques provide robustness against straggling servers in distributed computing, with the following limitations: First, they increase decoding complexity. Second, they ignore computations carried out by straggling…

Machine Learning · Computer Science 2018-11-29 Emre Ozfatura , Sennur Ulukus , Deniz Gunduz

In this paper, we study FPGA based pipelined and superscalar design of two variants of conjugate gradient methods for solving Laplacian equation on a discrete grid; the first version corresponds to the original conjugate gradient algorithm,…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-03-13 Sahithi Rampalli , Natasha Sehgal , Ishita Bindlish , Tanya Tyagi , Pawan Kumar

Distributed training of deep nets is an important technique to address some of the present day computing challenges like memory consumption and computational demands. Classical distributed approaches, synchronous or asynchronous, are based…

Machine Learning · Computer Science 2019-01-14 Youjie Li , Mingchao Yu , Songze Li , Salman Avestimehr , Nam Sung Kim , Alexander Schwing

In recent years, topology optimization has been developed sufficiently and many researchers have concentrated on enhancing to computationally numerical algorithms for computational effectiveness of this method. Along with the development of…

Numerical Analysis · Mathematics 2023-01-19 Nam G. Luu , Thanh T. Banh

Iterative methods for solving large sparse systems of linear equations are widely used in many HPC applications. Extreme scaling of these methods can be difficult, however, since global communication to form dot products is typically…

Mathematical Software · Computer Science 2020-09-29 Nick Brown , J. Mark Bull , Iain Bethune

We present an iterative method to diagonalise large matrices. The basic idea is the same as the conjugated gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroduce errors to the directions of…

Computational Physics · Physics 2009-11-10 Quanlin Jie , Dunhuan Liu

We consider the problem of how to reduce the cost of communication that is required for the parallel training of a neural network. The state-of-the-art method, Bulk Synchronous Parallel Stochastic Gradient Descent (BSP-SGD), requires many…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-04-18 Linnan Wang , Wei Wu , George Bosilca , Richard Vuduc , Zenglin Xu

Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…

Machine Learning · Computer Science 2025-11-21 Alan Yufei Dong , Jihao Andreas Lin , José Miguel Hernández-Lobato

The conjugate gradient (CG) method is an efficient iterative method for solving large-scale strongly convex quadratic programming (QP). In this paper we propose some generalized CG (GCG) methods for solving the $\ell_1$-regularized…

Optimization and Control · Mathematics 2016-02-15 Zhaosong Lu , Xiaojun Chen

This paper proposes a generalization of the conjugate gradient (CG) method used to solve the equation $Ax=b$ for a symmetric positive definite matrix $A$ of large size $n$. The generalization consists of permitting the scalar control…

Numerical Analysis · Mathematics 2016-11-17 Amit Bhaya , Pierre-Alexandre Bliman , Guilherme Niedu , Fernando Pazos

Training large deep learning models at scale is very challenging. This paper proposes Chimera, a novel pipeline parallelism scheme which combines bidirectional pipelines for efficiently training large-scale models. Chimera is a synchronous…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-08-22 Shigang Li , Torsten Hoefler

This work studies gradient coding (GC) in the context of distributed training problems with unreliable communication. We propose cooperative GC (CoGC), a novel gradient-sharing-based GC framework that leverages cooperative communication…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-07-08 Shudi Weng , Ming Xiao , Chao Ren , Mikael Skoglund

Neural network (NN) accelerators with multi-chip-module (MCM) architectures enable integration of massive computation capability; however, they face challenges of computing resource underutilization and off-chip communication overheads.…

Hardware Architecture · Computer Science 2026-02-17 Zongle Huang , Hongyang Jia , Kaiwei Zou , Yongpan Liu

In massive multiple-input multiple-output (MIMO) systems, achieving high spectral efficiency (SE) often requires advanced precoding algorithms whose complexity scales rapidly with the number of antennas, limiting practical deployment. In…

Signal Processing · Electrical Eng. & Systems 2026-03-13 Seunghyeong Yoo , Mintaek Oh , Jeonghun Park , Namyoon Lee , Jinseok Choi

Distributed synchronous stochastic gradient descent has been widely used to train deep neural networks (DNNs) on computer clusters. With the increase of computational power, network communications generally limit the system scalability.…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-01-19 Shaohuai Shi , Xiaowen Chu , Bo Li