Connections Among Applied Computational Group Theory, Matrix Representations, and Parallel Computations

应用计算群理论、矩阵表示和并行计算之间的联系

• 批准号: 9732330
• 负责人: Gene Cooperman
• 金额: $ 13万
• 依托单位: Northeastern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-08-15 至 2001-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9732330&HistoricalAwards=false
• 关键词: Connections; Among; Applied; Computational; Group

The goals of this project are: (a) application of computational group theory to related areas, and (b) scalability of applications through parallelism. This is expected to be useful in areas of application including aspects of linear numerical analysis, search (especially in the presence of symmetry) and algorithmic parallelization. This work will take advantage of a sizable body of more mature and stable algorithms of computational group theory that has evolved in recent years. As an example, the techniques for finding invariant subspaces of matrices over finite fields (the meataxe and condensation) have matured in recent years, while invariant subspace techniques are of current interest for iterative techniques in numerical analysis. The relevant algorithms will be adapted to larger scale applications through the use of parallelism and of data structures adapted toward that parallelism. The TOP-C parallel methodology will be used to identify central, repetitive tasks. The portability of this methodology across C, LISP, GAP and other languages helps eliminate the continuing barriers to extensive use of parallelization.

该项目的目标是：(a) 将计算群理论应用于相关领域，以及 (b) 通过并行性实现应用程序的可扩展性。 预计这将在线性数值分析、搜索（尤其是存在对称性的情况下）和算法并行化等应用领域中发挥作用。 这项工作将利用近年来发展起来的大量更成熟、更稳定的计算群论算法。 例如，在有限域上寻找矩阵不变子空间（肉斧和凝结）的技术近年来已经成熟，而不变子空间技术目前在数值分析中的迭代技术中引起了人们的兴趣。 相关算法将通过使用并行性和适应并行性的数据结构来适应更大规模的应用。 TOP-C 并行方法将用于识别中心、重复性任务。 这种方法在 C、LISP、GAP 和其他语言之间的可移植性有助于消除广泛使用并行化的持续障碍。