Related papers: The Communication-Hiding Conjugate Gradient Method…
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.…
Pipeline Parallelism (PP) enables large neural network training on small, interconnected devices by splitting the model into multiple stages. To maximize pipeline utilization, asynchronous optimization is appealing as it offers 100%…
Krylov methods provide a fast and highly parallel numerical tool for the iterative solution of many large-scale sparse linear systems. To a large extent, the performance of practical realizations of these methods is constrained by the…
Gradient descent (GD) methods are commonly employed in machine learning problems to optimize the parameters of the model in an iterative fashion. For problems with massive datasets, computations are distributed to many parallel computing…
To reduce the long training time of large deep neural network (DNN) models, distributed synchronous stochastic gradient descent (S-SGD) is commonly used on a cluster of workers. However, the speedup brought by multiple workers is limited by…
Krylov subspace, which is generated by multiplying a given vector by the matrix of a linear transformation and its successive powers, has been extensively studied in classical optimization literature to design algorithms that converge…
Most current prevalent iterative methods can be classified into the so-called extended Krylov subspace methods, a class of iterative methods which do not fall into this category are also proposed in this paper. Comparing with traditional…
Graph Convolutional Networks (GCNs) is the state-of-the-art method for learning graph-structured data, and training large-scale GCNs requires distributed training across multiple accelerators such that each accelerator is able to hold a…
Preconditioned Krylov subspace (KSP) methods are widely used for solving large-scale sparse linear systems arising from numerical solutions of partial differential equations (PDEs). These linear systems are often nonsymmetric due to the…
A Crank-Nicolson finite volume approximation for three-dimensional conservative space-fractional diffusion equation results in large and dense three-level Toeplitz discrete linear systems. Preconditioned Krylov subspace methods with sine…
In this paper we introduce a parameter dependent class of Krylov-based methods, namely CD, for the solution of symmetric linear systems. We give evidence that in our proposal we generate sequences of conjugate directions, extending some…
Context. Numerical solutions to transfer problems of polarized radiation in solar and stellar atmospheres commonly rely on stationary iterative methods, which often perform poorly when applied to large problems. In recent times, stationary…
Split learning (SL) offloads main computing tasks from multiple resource-constrained user equippments (UEs) to the base station (BS), while preserving local data privacy. However, its computation and communication processes remain…
Krylov subspace methods are extensively used in scientific computing to solve large-scale linear systems. However, the performance of these iterative Krylov solvers on modern supercomputers is limited by expensive communication costs. The…
Recently, a new variant of the BiCGStab method, known as the pipeline BiCGStab, has been proposed. This method can achieve a higher degree of scalability and speed-up rates through a mechanism in which the communication phase for the…
Pipelined Krylov methods seek to ameliorate the latency due to inner products necessary for projection by overlapping it with the computation associated with sparse matrix-vector multiplication. We clarify a folk theorem that this can only…
Subgraph counting aims to count the number of occurrences of a subgraph T (aka as a template) in a given graph G. The basic problem has found applications in diverse domains. The problem is known to be computationally challenging - the…
Krylov subspace methods are a powerful family of iterative solvers for linear systems of equations, which are commonly used for inverse problems due to their intrinsic regularization properties. Moreover, these methods are naturally suited…
Krylov subspace methods, such as the Conjugate Gradient (CG) and BiCGSTAB methods, are widely used in scientific computing for solving linear systems. In this study, we propose a new framework for solving large Sylvester equations in a…
We present a variant of the s-step Preconditioned Conjugate Gradient (PCG) method that combines a Chebyshev-stabilized Krylov basis with a Forward Gauss-Seidel (FGS) iteration for the solution of the reduced Gram systems. In s-step…