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

这个项目的目标是：（a）计算群论的相关领域的应用，和（B）通过并行的应用程序的可扩展性。 预计这将是有用的应用领域，包括方面的线性数值分析，搜索（特别是在对称性的存在）和算法并行化。 这项工作将利用一个相当大的机构更成熟和稳定的算法计算群论，近年来已经发展。 例如，寻找有限域上矩阵的不变子空间的技术（meataxe和condensation）近年来已经成熟，而不变子空间技术是数值分析中迭代技术的当前兴趣。 通过使用并行性和适应于该并行性的数据结构，相关算法将适于更大规模的应用。 TOP-C平行方法将用于确定中心的重复性任务。 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。

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.