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

该项目的目标是：(A)将计算群论应用于相关领域，以及(B)通过并行性实现应用程序的可扩展性。这有望在包括线性数值分析、搜索(特别是在存在对称性的情况下)和算法并行化等方面的应用领域有用。这项工作将利用近年来发展起来的大量更成熟和更稳定的计算群论算法。例如，求有限域上矩阵的不变子空间(Meataxa和凝聚)的技术近年来已经成熟，而不变子空间技术是当前数值分析中迭代技术的研究热点。相关算法将通过使用并行性和适应于该并行性的数据结构来适应更大规模的应用。将使用TOP-C并行方法来确定中心的重复性任务。这种方法跨C、LISP、GAP和其他语言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.