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In this paper we describe a parallel Gaussian elimination algorithm for matrices with entries in a finite field. Unlike previous approaches, our algorithm subdivides a very large input matrix into smaller submatrices by subdividing both…

Rings and Algebras · Mathematics 2018-06-13 Stephen Linton , Gabriele Nebe , Alice Niemeyer , Richard Parker , Jon Thackray

Accelerators for sparse matrix multiplication are important components in emerging systems. In this paper, we study the main challenges of accelerating Sparse Matrix Multiplication (SpMM). For the situations that data is not stored in the…

Hardware Architecture · Computer Science 2019-06-04 Pareesa Ameneh Golnari , Sharad Malik

This paper addresses spatial programming of sparse matrix computations for productive performance. The challenge is how to express an irregular computation and its optimizations in a regular way. A sparse matrix has (non-zero) values and a…

Mathematical Software · Computer Science 2018-10-18 Hongbo Rong

This article presents a new method to compute matrices from numerical simulations based on the ideas of sparse sampling and compressed sensing. The method is useful for problems where the determination of the entries of a matrix constitutes…

Chemical Physics · Physics 2014-10-21 Jacob N. Sanders , Xavier Andrade , Alán Aspuru-Guzik

Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-01-08 Austin R. Benson , Grey Ballard

This paper develops column partition based distributed schemes for a class of large-scale convex sparse optimization problems, e.g., basis pursuit (BP), LASSO, basis pursuit denosing (BPDN), and their extensions, e.g., fused LASSO. We are…

Optimization and Control · Mathematics 2020-03-18 Jinglai Shen , Jianghai Hu , Eswar Kumar Hathibelagal Kammara

Graph-based representations underlie a wide range of scientific problems. Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-12-14 Bruno Magalhaes , Felix Schürmann

We consider the co-design problem of sparse output feedback and row/column-sparse output matrix. A row-sparse (resp. column-sparse) output matrix implies a small number of outputs (resp. sensor measurements). We impose…

Optimization and Control · Mathematics 2017-06-27 Fu Lin , Veronica Adetola

We propose Rosko -- row skipping outer products -- for deriving sparse matrix multiplication (SpMM) kernels in reducing computation and memory access requirements of deep neural networks (DNNs). Rosko allows skipping of entire row…

Machine Learning · Computer Science 2023-07-11 Vikas Natesh , Andrew Sabot , H. T. Kung , Mark Ting

In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…

Numerical Analysis · Mathematics 2024-03-12 Hongyaoxing Gu

We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…

Symbolic Computation · Computer Science 2018-02-08 Daniel S. Roche

We implement two novel algorithms for sparse-matrix dense-matrix multiplication (SpMM) on the GPU. Our algorithms expect the sparse input in the popular compressed-sparse-row (CSR) format and thus do not require expensive format conversion.…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-06-13 Carl Yang , Aydin Buluc , John D. Owens

A common problem in large-scale data analysis is to approximate a matrix using a combination of specifically sampled rows and columns, known as CUR decomposition. Unfortunately, in many real-world environments, the ability to sample…

Machine Learning · Statistics 2018-07-10 Urvashi Oswal , Swayambhoo Jain , Kevin S. Xu , Brian Eriksson

We consider the problem of secure distributed matrix multiplication in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We show how to construct polynomial schemes for the outer…

Information Theory · Computer Science 2024-05-13 Ryann Cartor , Rafael G. L. D'Oliveira , Salim El Rouayheb , Daniel Heinlein , David Karpuk , Alex Sprintson

We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. We follow the idea of…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-03-06 Michael Lass , Stephan Mohr , Hendrik Wiebeler , Thomas D. Kühne , Christian Plessl

Scaling up the sparse matrix-vector multiplication kernel on modern Graphics Processing Units (GPU) has been at the heart of numerous studies in both academia and industry. In this article we present a novel non-parametric, self-tunable,…

Numerical Analysis · Computer Science 2012-12-24 Xintian Yang , Srinivasan Parthasarathy , Ponnuswamy Sadayappan

We propose a method for strict error control in sparse approximate matrix-matrix multiplication. The method combines an error bound and a parameter sweep to select an appropriate threshold value. The scheme for error control and the sparse…

Numerical Analysis · Mathematics 2021-06-02 Anton G. Artemov , Emanuel H. Rubensson

The research in parallel machine scheduling in combinatorial optimization suggests that the desirable parallel efficiency could be achieved when the jobs are sorted in the non-increasing order of processing times. In this paper, we find…

Numerical Analysis · Mathematics 2012-02-15 Lei Wang , Heng Liang , Fengshan Bai , Yan Huo

Parallel matrix multiplication is one of the most studied fundamental problems in distributed and high performance computing. We obtain a new parallel algorithm that is based on Strassen's fast matrix multiplication and minimizes…

Data Structures and Algorithms · Computer Science 2012-02-16 Grey Ballard , James Demmel , Olga Holtz , Benjamin Lipshitz , Oded Schwartz

Artificial intelligence workloads, especially transformer models, exhibit emergent sparsity in which computations perform selective sparse access to dense data. The workloads are inefficient on hardware designed for dense computations and…

Data Structures and Algorithms · Computer Science 2024-02-23 Brian Wheatman , Meghana Madhyastha , Randal Burns