Mathematical Sciences: Algorithms and Programs for Fourier Transforms and Crystallography

数学科学：傅里叶变换和晶体学的算法和程序

• 批准号: 9014947
• 负责人: James Cooley
• 金额: $ 3.4万
• 依托单位: IBM Thomas J Watson Research Center
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9014947&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algorithms; Programs; Fourier

This Small Grant for Exploratory Research will support mathematical research on general mathematical structures for fast Fourier transforms algorithms. The focus will be on computing the discrete Fourier transform for the general case. Applications to data possessing crystallographic symmetries will be made. Studies on related fast convolution algorithms will also be made. Data transformation and permutation algorithms will be produced. These be necessary for transforming data between stages of the Fourier transforms and for reducing and expanding data for input and output. Algorithms will be adapted to machine architectures including those of vector, parallel and hierarchical memory machines. They will take account of data flow, data permutations and data access in large scale computations. Group theoretical methods will play an important part in this effort. Included in the work is the goal of a systematic classification of the symmetries of all crystallographic groups. Algorithms and programs for others parts of the crystallographic calculation, particularly the refinement problem, will be produced. Implementation of this work in one large general crystallographic program package and report on the efficiency is planned.

这笔探索性研究的小额资助将支持对快速傅里叶变换算法的通用数学结构的数学研究。 重点是计算一般情况下的离散傅立叶变换。 将应用于具有晶体学对称性的数据。 相关快速卷积算法也将进行研究。 将产生数据转换和排列算法。这些对于在傅里叶变换的阶段之间变换数据以及减少和扩展输入和输出的数据是必要的。 算法将适应机器架构，包括向量、并行和分层存储机器。 他们将考虑大规模计算中的数据流、数据排列和数据访问。 群理论方法将在这项工作中发挥重要作用。 这项工作的目标是对所有晶体群的对称性进行系统分类。 将产生晶体学计算其他部分的算法和程序，特别是细化问题。 计划在一个大型通用晶体学程序包中实施这项工作并报告效率。