相关论文: Exploiting Multiple Levels of Parallelism in Spars…

We present the first parallel algorithm for solving systems of linear equations in symmetric, diagonally dominant (SDD) matrices that runs in polylogarithmic time and nearly-linear work. The heart of our algorithm is a construction of a…

Sparse matrix vector multiplication (SpMV) is a fundamental kernel in scientific codes that rely on iterative solvers. In this first part of our work, we present both a sequential and a basic MPI parallel implementations of SpMV, aiming to…

In this paper we introduce a generic model for multiplicative algorithms which is suitable for the MapReduce parallel programming paradigm. We implement three typical machine learning algorithms to demonstrate how similarity comparison,…

We introduce an algorithm for efficiently representing convolution with zero-padding and stride as a sparse transformation matrix, applied to a vectorized input through sparse matrix-vector multiplication (SpMV). We provide a theoretical…

Several manufacturers have already started to commercialize near-bank Processing-In-Memory (PIM) architectures. Near-bank PIM architectures place simple cores close to DRAM banks and can yield significant performance and energy improvements…

The Simplex tableau has been broadly used and investigated in the industry and academia. With the advent of the big data era, ever larger problems are posed to be solved in ever larger machines whose architecture type did not exist in the…

Since its introduction in 2004, the MapReduce framework has become one of the standard approaches in massive distributed and parallel computation. In contrast to its intensive use in practise, theoretical footing is still limited and only…

Matrix multiplication computation acceleration has been a research hotspot across various domains. Due to the characteristics of some applications, approximate matrix multiplication can achieve significant performance improvements without…

Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental operation in graph computing and analytics. However, the irregularity of real-world graphs poses significant challenges to achieving efficient SpMM operation for graph data on…

The sparse matrix-vector multiplication (SpMxV) is a kernel operation widely used in iterative linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers. Matrices with irregular sparsity patterns…

One of the most important and commonly used operations in many linear algebra functions is matrix-matrix multiplication (GEMM), which is also a key component in obtaining high performance of many scientific codes. It is a computationally…

General Matrix Multiplication (GEMM) is a critical kernel in high-performance computing and deep learning. While modern architectures like ARM's Scalable Matrix Extension (SME) introduce dedicated hardware for matrix operations, existing…

Recent architectures integrate high-performance and power-efficient matrix engines. These engines demonstrate remarkable performance in low-precision matrix multiplication, which is crucial in deep learning. Several techniques have been…

In this paper, we focus on three sparse matrix operations that are relevant for machine learning applications, namely, the sparse-dense matrix multiplication (SPMM), the sampled dense-dense matrix multiplication (SDDMM), and the composition…

We address the communication overhead of distributed sparse matrix-(multiple)-vector multiplication in the context of large-scale eigensolvers, using filter diagonalization as an example. The basis of our study is a performance model which…

Sparse matrix-vector multiplication (spMVM) is the dominant operation in many sparse solvers. We investigate performance properties of spMVM with matrices of various sparsity patterns on the nVidia "Fermi" class of GPGPUs. A new "padded…

Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…

Sparse matrix-vector multiplication (SpMxV) is a kernel operation widely used in iterative linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers. Matrices with irregular sparsity patterns make it…

This paper is concerned with developing an efficient numerical algorithm for fast implementation of the sparse grid method for computing the $d$-dimensional integral of a given function. The new algorithm, called the MDI-SG ({\em multilevel…

Sparse Ternary General Matrix-Matrix Multiplication (GEMM) remains under-optimized in existing libraries for Apple Silicon CPUs. We present a Sparse Ternary GEMM kernel optimized specifically for Apple's M-series processors. We propose a…