检索结果-内蒙古大学图书馆

matrix computations ON SYSTOLIC-TYPE MESHES - AN INTRODUCTION TO THE MULTIMESH GRAPH METHOD

COMPUTER 1990年第4期23卷 32-52页

作者： MORENO, JH LANG, T UNIV CONCEPCION DEPT ELECT ENGN CONCEPCION CHILE

Systolic-type arrays use both the fine-grain parallelism and the regularity of matrix computations effectively. The multimesh graph method for deriving these arrays is systematic, flexible, and easy to use

关键词： cellular arrays fine-grain parallelism graph theory matrix algebra matrix computations multimesh graph method parallel processing regularity systolic arrays systolic-type meshes

来源：评论

学校读者我要写书评

暂无评论

matrix computations and Optimization in Apache Spark 16

Matrix Computations and Optimization in Apache Spark

引用

22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD)

作者： Zadeh, Reza Bosagh Meng, Xiangrui Ulanov, Alexander Yavuz, Burak Pu, Li Venkataraman, Shivaram Sparks, Evan Staple, Aaron Zaharia, Matei Stanford & Matroid 475 Via Ortega Stanford CA 94305 USA Databricks 160 Spear St13th Floor San Francisco CA 94105 USA HP Labs 1501 Page Mill Rd Palo Alto CA 94304 USA Twitter 1355 Market St Suite 900 San Francisco CA 94103 USA Univ Calif Berkeley 465 Soda Hall Berkeley CA 94720 USA Databricks 160 Spear St13th Floor San Francisco CA 94105 USA

ISBN: (纸本)9781450342322

We describe matrix computations available in the cluster programming framework, Apache Spark. Out of the box, Spark provides abstractions and implementations for distributed matrices and optimization routines using these matrices. When translating single-node algorithms to run on a distributed cluster, we observe that often a simple idea is enough: separating matrix operations from vector operations and shipping the matrix operations to be ran on the cluster, while keeping vector operations local to the driver. In the case of the Singular Value Decomposition, by taking this idea to an extreme, we are able to exploit the computational power of a cluster, while running code written decades ago for a single core. Another example is our Spark port of the popular TFOCS optimization package, originally built for MATLAB, which allows for solving Linear programs as well as a variety of other convex programs. We conclude with a comprehensive set of benchmarks for hardware accelerated matrix computations from the JVM, which is interesting in its own right, as many cluster programming frameworks use the JVM. The contributions described in this paper are already merged into Apache Spark and available on Spark installations by default, and commercially supported by a slew of companies which provide further services.

关键词： Distributed Linear Algebra matrix computations Optimization Machine Learning MLlib Spark

来源：评论

学校读者我要写书评

暂无评论

Additive preconditioning and aggregation in matrix computations

引用

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2008年第8期55卷 1870-1886页

作者： Pan, Victor Y. Ivolgin, Dmitriy Murphy, Brian Rosholt, Rhys Eric Taj-Eddin, Islam Tang, Yuqing Yan, Xiaodong CUNY Lehman Coll Dept Math & Comp Sci Bronx NY 10468 USA CUNY Phd Program Comp Sci New York NY 10036 USA CUNY Phd Program Math & Comp Sci New York NY 10036 USA

We combine our novel SVD-free additive preconditioning with aggregation and other relevant techniques to facilitate the solution of a linear system of equations and other fundamental matrix computations. Our analysis and experiments show the power of our algorithms, guide us in selecting most effective policies of preconditioning and aggregation, and provide some new insights into these and related subjects. Compared to the popular SVD-based multiplicative preconditioners, our additive preconditioners are generated more readily and for a much larger class of matrices. Furthermore, they better preserve matrix structure and sparseness and have a wider range of applications (e.g., they facilitate the solution of a consistent singular linear system of equations and of the eigenproblem). (C) 2007 Elsevier Ltd. All rights reserved.

关键词： matrix computations additive preconditioning aggregation MSAs

来源：评论

学校读者我要写书评

暂无评论

Additive preconditioning for matrix computations

引用

LINEAR ALGEBRA AND ITS APPLICATIONS 2010年第4期432卷 1070-1089页

作者： Pan, Victor Y. Ivolgin, Dmitriy Murphy, Brian Rosholt, Rhys Eric Tang, Yuqing Yan, Xiaodong CUNY Herbert H Lehman Coll Dept Math & Comp Sci Bronx NY 10468 USA CUNY PhD Program Comp Sci New York NY 10036 USA

Our randomized additive preconditioners are readily available and regularly facilitate the solution of linear systems of equations and eigen-solving for a very large class of input matrices. We study the generation of such preconditioners and their impact on the rank and the condition number of a matrix. We also propose some techniques for their refinement and two alternative versions of randomized preprocessing. Our analysis and experiments show the power of our approach even where we employ weak randomization, that is generate sparse and structured preconditioners, defined by a small number of random parameters. (C) 2009 Elsevier Inc. All rights reserved.

关键词： matrix computations Additive preconditioning Weak randomization

来源：评论

学校读者我要写书评

暂无评论

COMMUNICATION AND matrix computations ON LARGE MESSAGE PASSING SYSTEMS

引用

PARALLEL COMPUTING 1990年第1期16卷 27-40页

作者： STEWART, GW UNIV MARYLAND INST ADV COMP STUDIESCOLLEGE PKMD 20742

This paper is concerned with the consequences for matrix computations of having a rather large number of general purpose processors, say ten or twenty thousand, connected in a network in such a way that a processor can communicate only with its immediate neighbors. Certain communication tasks associated with most matrix algorithms are defined and formulas developed for the time required to performs them under several communication regimes. The results are compared with the times for a nominal n 3 floating point operations. The results suggest that it is possible to use a large number of processors to solve matrix problems at a relatively fine granularity, provided fine grain communication is available.

关键词： Communication costs Communication tasks matrix computations matrix distribution Message passing systems Timing analysis

来源：评论

学校读者我要写书评

暂无评论

UPCBLAS: a library for parallel matrix computations in Unified Parallel C

引用

CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE 2012年第14期24卷 1645-1667页

作者： Gonzalez-Dominguez, Jorge Martin, Maria J. Taboada, Guillermo L. Tourino, Juan Doallo, Ramon Mallon, Damian A. Wibecan, Brian Univ A Coruna Comp Architecture Grp La Coruna Spain Galicia Supercomp Ctr CESGA Santiago De Compostela Spain

The popularity of Partitioned Global Address Space (PGAS) languages has increased during the last years thanks to their high programmability and performance through an efficient exploitation of data locality, especially on hierarchical architectures such as multicore clusters. This paper describes UPCBLAS, a parallel numerical library for dense matrix computations using the PGAS Unified Parallel C language. The routines developed in UPCBLAS are built on top of sequential basic linear algebra subprograms functions and exploit the particularities of the PGAS paradigm, taking into account data locality in order to achieve a good performance. Furthermore, the routines implement other optimization techniques, several of them by automatically taking into account the hardware characteristics of the underlying systems on which they are executed. The library has been experimentally evaluated on a multicore supercomputer and compared with a message-passing-based parallel numerical library, demonstrating good scalability and efficiency. Copyright (c) 2012 John Wiley & Sons, Ltd.

关键词： Parallel Library matrix computations PGAS UPC BLAS

来源：评论

学校读者我要写书评

暂无评论

Systematic Analysis of Low-Precision Training in Deep Neural Networks: Factors Influencing matrix computations

引用

APPLIED SCIENCES-BASEL 2024年第21期14卷 10025页

作者： Shen, Ao Lai, Zhiquan Zhang, Lizhi Natl Univ Def Technol Natl Key Lab Parallel & Distributed Comp Changsha 410073 Peoples R China

As Deep Neural Networks (DNNs) continue to increase in complexity, the computational demands of their training have become a significant bottleneck. Low-precision training has emerged as a crucial strategy, wherein full-precision values are quantized to lower precisions, reducing computational overhead while aiming to maintain model accuracy. While prior research has primarily focused on minimizing quantization noise and optimizing performance for specific models and tasks, a comprehensive understanding of the general principles governing low-precision computations across diverse DNN architectures has been lacking. In this paper, we address this gap by systematically analyzing the factors that influence low-precision matrix computations, which are fundamental to DNN training. We investigate three critical factors-accumulation in matrix calculations, the frequency of element usage, and the depth of matrices within the model-and their impact on low-precision training. Through controlled experiments on standard models, as well as customized experiments designed to isolate individual factors, we derive several key insights: layers with higher accumulation and matrices with lower usage frequencies demonstrate greater tolerance to low-precision noise, without significantly compromising the stability of model training. Additionally, while the depth of matrices influences the stability of matrix operations to some extent, it does not have a noticeable effect on the overall training outcomes. Our findings contribute to the development of generalizable principles for low-precision training, offering a systematic framework applicable across various DNN architectures. We provide empirical evidence supporting the strategic allocation of training bit-widths based on the analyzed factors, thereby enhancing the efficiency and effectiveness of DNN training in resource-constrained environments.

关键词： low-precision training quantization noise matrix computations training efficiency accumulation frequency depth

来源：评论

学校读者我要写书评

暂无评论

A new highly convergent Monte Carlo method for matrix computations

引用

MATHEMATICS AND COMPUTERS IN SIMULATION 1998年第2-5期47卷 165-181页

作者： Dimov, IT Alexandrov, VN Bulgarian Acad Sci Ctr Informat & Comp Technol Sofia 1113 Bulgaria Univ Liverpool Dept Comp Sci Liverpool Merseyside England

In this paper a second degree iterative Monte Carlo method for solving systems of linear algebraic equations and matrix inversion is presented. Comparisons are made with iterative Monte Carlo methods with degree one. It is shown that the mean value of the number of chains N, and the chain length T, required to reach given precision can be reduced. The following estimate on N is obtained: N = N-c/(c(N) + bN(c)(1/2))(2), where N-c is the number of chains in the usual degree one method. In addition it is shown that b>0 and that N < N-c/c(N)(2). This result shows that for our method the number of realizations N can be at least c(N)(2) times less than the number of realizations N-c of the existing Monte Carlo method. For parallel implementation, i.e. regular arrays or MIMD distributed memory architectures, these results imply faster algorithms and the reduction of the size of the arrays. This leads also in applying such methods to the problems with smaller sizes, since until now Monte Carlo methods are applicable for large scale problems and when the component of the solution vector or element or row of the inverse matrix has to be found. (C) 1998 IMACS/Elsevier Science B.V.

关键词： Monte Carlo method matrix computations convergence eigenvalues convergent iterative process parallel computation

来源：评论

学校读者我要写书评

暂无评论

COMPLEXITY OF PARALLEL matrix computations

引用

THEORETICAL COMPUTER SCIENCE 1987年第1期54卷 65-85页

作者： PAN, V Computer Science Department State University of New York at Albany Albany NY12222 U.S.A.

We estimate parallel complexity of several matrix computations under both Boolean and arithmetic machine models using deterministic and probabilistic approaches. Those computations include the evaluation of the inverse, the determinant, and the characteristic polynomial of a matrix. Recently, processor efficiency of the previous parallel algorithms for numerical matrix inversion has been substantially improved in (Pan and Reif, 1987), reaching optimum estimates up to within a logarithmic factor; that work, however, applies neither to the evaluation of the determinant and the characteristic polynomial nor to exact matrix inversion nor to the numerical inversion of ill-conditioned matrices. We present four new approaches to the solution of those latter problems (having several applications to combinatorial computations) in order to extend the suboptimum time and processor bounds of (Pan and Reif, 1987) to the case of computing the inverse, determinant, and characteristic polynomial of an arbitrary integer input matrix. In addition, processor efficient algorithms using polylogarithmic parallel time are devised for some other matrix computations, such as triangular and QR -factorizations of a matrix and its reduction to Hessenberg form.

关键词： Parallel algorithms computational complexity matrix computations

来源：评论

学校读者我要写书评

暂无评论

Monte Carlo methods for matrix computations on the grid

引用

FUTURE GENERATION COMPUTER SYSTEMS-THE INTERNATIONAL JOURNAL OF ESCIENCE 2008年第6期24卷 605-612页

作者： Branford, S. Sahin, C. Thandavan, A. Weihrauch, C. Alexandrov, V. N. Dimov, I. T. Univ Reading Ctr Adv Comp & Emerging Technol Sch Syst Engn Reading RG6 6BX Berks England Bulgarian Acad Sci Inst Parallel Proc BU-1113 Sofia Bulgaria

Many scientific and engineering applications involve inverting large matrices or solving systems of linear algebraic equations. Solving these problems with proven algorithms for direct methods can take very long to compute, as they depend on the size of the matrix. The computational complexity of the stochastic Monte Carlo methods depends only on the number of chains and the length of those chains. The computing power needed by inherently parallel Monte Carlo methods can be satisfied very efficiently by distributed computing technologies such as Grid computing. In this paper we show how a load balanced Monte Carlo method for computing the inverse of a dense matrix can be constructed, show how the method can be implemented on the Grid, and demonstrate how efficiently the method scales on multiple processors. (C) 2007 Elsevier B.V. All rights reserved.

关键词： Monte Carlo methods matrix computations grid computing

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：