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解线性方程组的子域。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的方程的最简单和最常见的近似。这些系统的数值解通常被用来解决从结构工程到电磁辐射研究的各种问题。由于其无处不在的性质，用于解决这些问题的子程序库一直是计算科学中最重要(也是研究最多)的领域之一。这个项目扩展了这些最广泛使用的软件包之一-LAPACK项目-在下一代硬件上使用新的算法和Torun。这个项目将进行广泛的协同活动来设计和实现数值线性代数算法。它针对一系列稠密和稀疏的线性系统和特征值问题。总的目标是为这些问题提供最快、最准确的解决方案，并将它们提供给广泛和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Berkeley高性能计算环境)。事实上，许多拟议的研究都是出于这些社区的特殊应用需求。鉴于这些社区的规模和多样性，该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，研究人员的动机是迎接新体系结构在不断增长的使用中带来的机遇和挑战；除了前面提到的分布式环境，它们还包括SMP的集群(或“簇”)。

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").