Linear Algebra Algorithms and Tools for Emerging Computing Environments and User Communities

数值线性代数是在数字计算机上求解线性方程组的分支。这些系统出现在应用科学和工程的许多领域，因为线性方程是许多更复杂方程的最简单和最常见的近似。这些系统的数值解决方案通常用于解决从结构工程到电磁辐射研究的问题。由于它们无处不在的特性，用于解决这些问题的子程序库已成为计算科学中最重要（和研究最多）的领域之一。该项目扩展了这些软件包中最广泛使用的软件包之一LAPACK项目，以使用新算法并在下一代硬件上运行。这个项目将追求广泛的协同活动来设计和实现数值线性代数算法。它的目标是一系列密集和稀疏的线性系统和特征值问题。总体目标是为这些问题提供最快、最准确的解决方案，并将其提供给广泛且不断变化的用户社区。除了现有的大型LAPACK用户社区外，该软件还将作为网格服务提供给PACI、Millennium和ASCI用户社区（Millennium是伯克利高性能计算环境）。事实上，许多拟议的研究都是由这些社区的特殊应用需求驱动的。考虑到这些社区的规模和多样性，项目的一部分是教育性质的，使从专家到初学者的用户能够在丰富的可用工具中找到他们需要的东西。最后，研究人员有动力去迎接新架构在日益增长的使用中的机遇和挑战；除了前面提到的分布式环境之外，它们还包括smp集群（或“丛集”）。

Numerical linear algebra is the subfield that solves systems of linearequations on digital computers. These systems appear in many fields ofapplied science and engineering, as linear equations are the simplest andmost common approximation to many more complex equations. Numericalsolutions to these systems are routinely used to solve problems rangingfrom structural engineering to electromagnetic radiation studies. Becauseof their ubiquitous nature, subroutine libraries for solving these problemsHas been one of the most important (and most studied) areas incomputational science. This project extends one of the most widely-used ofthese software packages - the LAPACK project - to use new algorithms and torun on the next generation of hardware.This project will pursue a broad range of synergistic activities to designand implement numerical linear algebra algorithms. It targets a range ofdense and sparse linear systems and eigenvalue problems. The overall goalis to produce the fastest and most accurate solvers for these problems, andmake them available to a broad and changing user community. Besides theexisting large LAPACK user community, the software will be made availableas a Grid-enabled service to the PACI, Millennium and ASCI user communities(Millennium is the Berkeley high performance computing environment).Indeed, much of the proposed research is motivated by particularapplications demands from these communities. Given the size and diversityof these communities, part of the project is educational in nature, toenable users from experts to beginning students to find what they needamong the wealth of tools available. Finally, the researchers are motivatedto meet the opportunities and challenges of new architectures in growinguse; besides the distributed environment mentioned before, they includeclusters of SMPs (or "CLUMPs").