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区域会议 #9414856“Numerical Linear Algebra on Parallel Processors” 在科学和工程的大多数分支中，数值线性代数在计算机解决问题中起着核心作用。 这是因为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它们。 因此，相当多的注意力一直致力于发展有效的方法来解决线性代数问题的计算机上。 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，因为许多在传统计算机上使用的方法在并行机上使用时效率低下。由于研究的增长，研究人员和学生很难跟上最新的技术水平。因此，非常需要有人对当前的技术水平和预期的未来发展提供全面的看法。 这种全面的观点现在特别重要，因为对于并行机的架构有一个相当清晰的共识，并且对于与软件相关的许多问题也有一个正在形成的共识。 为了提供这样一个全面的看法并行数值线性代数和刺激进一步的研究领域，NSF/CBMS区域会议将举行在弗朗西斯科大学在1995年6月12日的一周，教授詹姆斯W。德梅尔担任首席讲师。 Demmel教授将开始讨论并行架构和并行软件。他将继续讨论稠密矩阵的并行算法。这将包括矩阵乘法，高斯消除，最小二乘问题的解决方案和计算特征值和特征向量的并行算法的讨论。他还将讲授稀疏矩阵的并行算法。这些讲座将涵盖直接和迭代方法;他们将讨论稀疏矩阵的分割算法，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的讲座补充。这些补充讲座将涵盖矩阵分解，区域分解方法，并行有限元，图分割和应用的多前沿方法。

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.