Mathematical Sciences: NSF/CBMS Regional Conference in the Mathematical Sciences - Numerical Linear Algebra on ParallelProcessors - June 12 - 16, 1995

帕切科摘要：NSF/CBMS地区会议#9414856“并行处理机上的数值线性代数”在大多数科学和工程分支中，数值线性代数在用计算机解决问题中起着核心作用。这样做的原因是，科学家和工程师通常通过将非线性问题简化为一系列线性问题来解决这些问题。因此，在计算机上解决线性代数问题的有效方法的发展受到了相当大的关注。在过去的十年里，并行处理的出现导致了数值线性代数研究的巨大额外增长，因为在传统计算机上使用的许多方法在并行机上使用时效率低下。作为研究增长的结果，研究人员和学生很难跟上最先进的技术。因此，非常需要有人对当前的技术状态和预期的未来发展提供全面的看法。这一全面的观点现在尤其重要，因为关于并行机的体系结构已经有了相当明确的共识，并且在与软件相关的许多问题上也出现了共识。为了提供对并行数值线性代数的全面看法并促进对该领域的进一步研究，将于1995年6月12日在旧金山大学举行一次NSF/CBMS区域会议，由James W.Demmel教授担任主要讲师。Demmel教授将首先讨论并行体系结构和并行软件。他将继续讨论稠密矩阵的并行算法。这将包括对矩阵乘法、高斯消去法、最小二乘问题的求解以及特征值和特征向量的计算的并行算法的讨论。他还将讲授稀疏矩阵的并行算法。这些讲座将包括直接方法和迭代方法；他们将讨论划分稀疏矩阵的算法、Cholesky分解、GMRES、QMR以及Lanczos和Arnoldi方法。德梅尔教授的演讲将辅之以该领域其他几位专家的演讲。这些补充讲座将涵盖矩阵因式分解的多前沿方法、区域分解方法、并行有限元、图形划分和应用。

Pacheco ABSTRACT: NSF/CBMS Regional Conference #9414856 "Numerical Linear Algebra on Parallel Processors" In most branches of science and engineering, numerical linear algebra plays a central role in the solution of problems by computer. The reason for this is that scientists and engineers usually solve nonlinear problems by reducing them to a sequence of linear problems. Thus considerable attention has been devoted to the development of efficient methods for solving problems in linear algebra on computers. Within the last ten years, the advent of parallel processing has resulted in enormous additional growth in research into numerical linear algebra, since many of the methods used on conventional computers are inefficient when used on parallel machines. As a consequence of this growth in research, it is extremely difficult for researchers and students to keep abreast of the state of the art. Thus there is a great need for someone to provide a comprehensive view of the current state of the art and anticipated future developments. This comprehensive view is especially important now because there is a fairly clear consensus about architectures for parallel machines and an emerging consensus about many issues related to software. In order to provide such a comprehensive view of parallel numerical linear algebra and to stimulate further research into the field, an NSF/CBMS Regional Conference will be held at the University of San Francisco during the week of June 12, 1995, with Professor James W. Demmel as the principal lecturer. Professor Demmel will begin by discussing parallel architectures and parallel software. He will continue with a discussion of parallel algorithms for dense matrices. This will include a discussion of parallel algorithms for matrix multiplication, Gaussian elimination, the solution of least squares problems and the calculation of eigenvalues and eigenvectors. He will also lecture on parallel algorithms for sparse ma trices. These lectures will cover direct and iterative methods; they will discuss algorithms for partitioning sparse matrices, Cholesky factorization, GMRES, QMR, and the Lanczos and Arnoldi methods. Professor Demmel's lectures will be supplemented by lectures by several other specialists in the field. These supplementary lectures will cover multifrontal methods for matrix factorization, domain decomposition methods, parallel finite elements, graph partitioning, and applications.