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

摘要：NSF/CBMS区域会议#9414856“并行处理器上的数值线性代数”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非线性问题。因此，在计算机上求解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增长，因为传统计算机上使用的许多方法在并行机器上使用时效率低下。由于研究的增长，研究人员和学生要跟上最新的技术发展是极其困难的。因此，非常需要有人对目前的技术状况和预期的未来发展提供一个全面的看法。这种全面的观点现在尤其重要，因为对于并行机器的体系结构已经有了相当明确的共识，并且对于与软件相关的许多问题也正在形成共识。为了提供平行数值线性代数的这样一个全面的观点，并刺激对该领域的进一步研究，一个NSF/CBMS区域会议将于1995年6月12日的那一周在旧金山大学举行，由James W. Demmel教授担任首席讲师。Demmel教授将首先讨论并行架构和并行软件。他将继续讨论密集矩阵的并行算法。这将包括讨论矩阵乘法的并行算法，高斯消去，最小二乘问题的解以及特征值和特征向量的计算。他还将讲授稀疏矩阵的并行算法。这些讲座将涵盖直接和迭代方法；他们将讨论稀疏矩阵的划分算法，Cholesky分解，GMRES， QMR，以及Lanczos和Arnoldi方法。Demmel教授的讲座将由该领域的其他几位专家进行补充。这些补充讲座将涵盖矩阵分解的多面方法、域分解方法、并行有限元、图划分和应用。

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.