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In this study, we propose a simple method for fault-tolerant Strassen-like matrix multiplications. The proposed method is based on using two distinct Strassen-like algorithms instead of replicating a given one. We have realized that using…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-10-11 Osman B. Guney , Suayb S. Arslan

Because of DNA appealing features as perfect material, including minuscule size, defined structural repeat and rigidity, programmable DNA-mediated processing is a promising computing paradigm, which employs DNAs as information storing and…

Biological Physics · Physics 2015-08-17 Jian-Jun Shu , Qi-Wen Wang , Kian-Yan Yong , Fangwei Shao , Kee Jin Lee

Efficient multiple precision linear numerical computation libraries such as MPLAPACK are critical in dealing with ill-conditioned problems. Specifically, there are optimization methods for matrix multiplication, such as the Strassen…

Numerical Analysis · Mathematics 2023-07-13 Tomonori Kouya

Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…

Materials Science · Physics 2009-10-31 D. R. Bowler , T. Miyazaki , M. J. Gillan

Fast approximations to matrix multiplication have the potential to dramatically reduce the cost of neural network inference. Recent work on approximate matrix multiplication proposed to replace costly multiplications with table-lookups by…

Machine Learning · Computer Science 2022-07-14 Calvin McCarter , Nicholas Dronen

Karppa & Kaski (2019) proposed a novel ``broken" or ``opportunistic" matrix multiplication algorithm, based on a variant of Strassen's algorithm, and used this to develop new algorithms for Boolean matrix multiplication, among other tasks.…

Data Structures and Algorithms · Computer Science 2024-09-05 David G. Harris

The growth of big data in domains such as Earth Sciences, Social Networks, Physical Sciences, etc. has lead to an immense need for efficient and scalable linear algebra operations, e.g. Matrix inversion. Existing methods for efficient and…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-01-16 Chandan Misra , Sourangshu Bhattacharya , Soumya K. Ghosh

We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of…

Numerical Analysis · Mathematics 2017-10-10 Lek-Heng Lim , Jonathan Weare

This paper presents an efficient technique for matrix-vector and vector-transpose-matrix multiplication in distributed-memory parallel computing environments, where the matrices are unstructured, sparse, and have a substantially larger…

Mathematical Software · Computer Science 2018-12-04 Jonathan Eckstein , Gyorgy Matyasfalvi

The inherent diversity of computation types within the deep neural network (DNN) models often requires a variety of specialized units in hardware processors, which limits computational efficiency, increasing both inference latency and power…

Machine Learning · Computer Science 2024-08-21 Ruiqi Sun , Siwei Ye , Jie Zhao , Xin He , Jianzhe Lin , Yiran Li , An Zou

The complexity of matrix multiplication (hereafter MM) has been intensively studied since 1969, when Strassen surprisingly decreased the exponent 3 in the cubic cost of the straightforward classical MM to log 2 (7) $\approx$ 2.8074.…

Symbolic Computation · Computer Science 2016-12-20 Jean-Guillaume Dumas , Victor Pan

Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due…

Mathematical Software · Computer Science 2016-11-04 Jianyu Huang , Leslie Rice , Devin A. Matthews , Robert A. van de Geijn

This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…

Symbolic Computation · Computer Science 2025-11-07 Jean-Guillaume Dumas , Bruno Grenet

DNA pattern matching is essential for many widely used bioinformatics applications. Disease diagnosis is one of these applications, since analyzing changes in DNA sequences can increase our understanding of possible genetic diseases. The…

Hardware Architecture · Computer Science 2022-06-01 Jinane Bazzi , Jana Sweidan , Mohammed E. Fouda , Rouwaida Kanj , Ahmed M. Eltawil

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,…

Data Structures and Algorithms · Computer Science 2011-12-05 Song Liu , Peter Flach , Nello Cristianini

It is well known that Strassen and Winograd algorithms can reduce the computational costs associated with dense matrix multiplication. We have already shown that they are also very effective for software-based multiple precision…

Numerical Analysis · Mathematics 2016-05-16 Tomonori Kouya

We present a very fast algorithm for general matrix factorization of a data matrix for use in the statistical analysis of high-dimensional data via latent factors. Such data are prevalent across many application areas and generate an…

The paper presents a parallel math library, dMath, that demonstrates leading scaling when using intranode, internode, and hybrid-parallelism for deep learning (DL). dMath provides easy-to-use distributed primitives and a variety of…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-11-24 Steven Eliuk , Cameron Upright , Hars Vardhan , Stephen Walsh , Trevor Gale

This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples…

Symbolic Computation · Computer Science 2024-07-02 Jean-Guillaume Dumas , Bruno Grenet

DNA-mediated computing is a novel technology that seeks to capitalize on the enormous informational capacity of DNA and has tremendous computational ability to compete with the current silicon-mediated computing, due to massive parallelism…

Emerging Technologies · Computer Science 2017-09-01 Jian-Jun Shu , Qi-Wen Wang , Kian-Yan Yong