Numerical Methods for Very Large Sparse Dynamical Systems

9405380博利这个项目将开发和实验的各种核心数值算法的大型稀疏或结构化线性代数问题。 研究的一部分是开发有效的算法，用于分析和设计非常大的控制模型，如与大型柔性空间结构相关的模型。 为了实现这一目标，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李雅普诺夫方程，大阶矩阵束，大的特征值和奇异值求解器。 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。 标准稀疏矩阵库（SPARSKIT）将用作软件开发的基础。 为了评估算法的有效性，将探讨从近似解获得的控制器设计的质量。 ***

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. ***