相关论文: Communication-hiding pipelined BiCGSafe methods fo…

A High Performance Computing alternative to traditional Krylov subspace methods, pipelined Krylov subspace solvers offer better scalability in the strong scaling limit compared to standard Krylov subspace methods for large and sparse linear…

Pipelined Krylov subspace methods avoid communication latency by reducing the number of global synchronization bottlenecks and by hiding global communication behind useful computational work. In exact arithmetic pipelined Krylov subspace…

In this article, we propose an accuracy-assuring technique for finding a solution for unsymmetric linear systems. Such problems are related to different areas such as image processing, computer vision, and computational fluid dynamics.…

Pipelined Krylov subspace methods (also referred to as communication-hiding methods) have been proposed in the literature as a scalable alternative to classic Krylov subspace algorithms for iteratively computing the solution to a large…

Parallel implementations of Krylov subspace methods often help to accelerate the procedure of finding an approximate solution of a linear system. However, such parallelization coupled with asynchronous and out-of-order execution often…

This paper presents performance results comparing MPI-based implementations of the popular Conjugate Gradient (CG) method and several of its communication hiding (or 'pipelined') variants. Pipelined CG methods are designed to efficiently…

With the increasing scale of models, the need for efficient distributed training has become increasingly urgent. Recently, many synchronous pipeline parallelism approaches have been proposed to improve training throughput. However, these…

ML(n)BiCGStab is a Krylov subspace method for the solution of large, sparse and non-symmetric linear systems. In theory, it is a method that lies between the well-known BiCGStab and GMRES/FOM. In fact, when n = 1, ML(1)BiCGStab is BiCGStab…

Krylov subspace methods are widely known as efficient algebraic methods for solving large scale linear systems. However, on massively parallel hardware the performance of these methods is typically limited by communication latency rather…

Krylov subspace methods are among the most efficient solvers for large scale linear algebra problems. Nevertheless, classic Krylov subspace algorithms do not scale well on massively parallel hardware due to synchronization bottlenecks.…

Implicit integration of the viscous term can significantly improve performance in computational fluid dynamics for highly viscous fluids such as lava. We show improvements over our previous proposal for semi-implicit viscous integration in…

Biclustering is a powerful unsupervised learning technique for simultaneously identifying coherent subsets of rows and columns in a data matrix, thus revealing local patterns that may not be apparent in global analyses. However, most…

Sparse inner product (SIP) has the attractive property of overhead being dominated by the intersection of inputs between parties, independent of the actual input size. It has intriguing prospects, especially for boosting machine learning on…

Consider a device that is connected to an edge processor via a communication channel. The device holds local data that is to be offloaded to the edge processor so as to train a machine learning model, e.g., for regression or classification.…

Krylov subspace recycling is a process for accelerating the convergence of sequences of linear systems. Based on this technique, the recycling BiCG algorithm has been developed recently. Here, we now generalize and extend this recycling…

By reducing the number of global synchronization bottlenecks per iteration and hiding communication behind useful computational work, pipelined Krylov subspace methods achieve significantly improved parallel scalability on present-day HPC…

We introduce the bilinear generalized vector approximate message passing (BiG-VAMP) algorithm which jointly recovers two matrices U and V from their noisy product through a probabilistic observation model. BiG-VAMP provides computationally…

This study is mainly focused on iterative solutions to shifted linear systems arising from a Quantum Chromodynamics (QCD) problem. To solve such system efficiently, we explore a kind of shifted QMRCGstab (SQMRCGstab) methods, which is…

We present variants of the Conjugate Gradient (CG), Conjugate Residual (CR), and Generalized Minimal Residual (GMRES) methods which are both pipelined and flexible. These allow computation of inner products and norms to be overlapped with…

The standard implementation of the conjugate gradient algorithm suffers from communication bottlenecks on parallel architectures, due primarily to the two global reductions required every iteration. In this paper, we study conjugate…