Numerical Methods for Very Large Sparse Dynamical Systems

超大型稀疏动力系统的数值方法

• 批准号: 9405380
• 负责人: Daniel Boley
• 金额: $ 18万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-09-15 至 1998-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9405380&HistoricalAwards=false
• 关键词: Numerical; Methods; Very; Large; Sparse

9405380 Boley This project will develop and experiment with a variety of core numerical algorithms for large sparse or structured linear algebra problems. Part of the research is the development of effective algorithms for the analysis and design of very large control models such as those related to large flexible space structures. To accomplish this, a major focus of this research will be the design of effective and efficient linear algebra algorithms. Examples of problems to be addressed are large Lyapunov equations, large order matrix pencils, large eigenvalue and singular values solvers. Parallel algorithms will be explored and exploited. Approximate solutions obtained via Krylov space methods, or other methods, will be analyzed. A standard sparse matrix library (SPARSKIT) will be used as the foundation for the software development. To evaluate the effectiveness of the algorithms, the quality of controller designs obtained from the approximate solutions will be explored. ***

9405380 Boley这个项目将开发和实验各种核心数值算法，用于大型稀疏或结构化线性代数问题。研究的一部分是开发用于分析和设计超大型控制模型的有效算法，例如与大型柔性空间结构相关的控制模型。为了实现这一点，本研究的一个主要重点将是设计有效和高效的线性代数算法。要解决的问题的例子是大型李雅普诺夫方程，大阶矩阵铅笔，大特征值和奇异值求解。并行算法将被探索和利用。将分析通过Krylov空间方法或其他方法获得的近似解。将使用标准稀疏矩阵库（SPARSKIT）作为软件开发的基础。为了评估算法的有效性，将探讨由近似解得到的控制器设计的质量。＊＊＊