Research Initiation Award: Numerical Solution of Large-Scale Algebraic Riccati Equations

研究启动奖：大规模代数 Riccati 方程的数值解

• 批准号: 9009483
• 负责人: Judith Gardiner
• 金额: $ 5.98万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 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: 1990-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9009483&HistoricalAwards=false
• 关键词: Research; Initiation; Award; Numerical; Solution

The development of parallel and vector algorithms for solving very large matrix algebraic Riccati equations is proposed. The approach to be used stresses the use of computational kernels such as the BLAS3, which are available on a wide variety of parallel computers. This approach will make the algorithms portable to many advanced scientific computers. Much of the research is based on the matrix sign function algorithm, an iterative method that has been shown to work well on a certain class of multiprocessor. Topics for research include easily parallelized "multiplication rich" algorithms, parallel and vector algorithms for several different advanced computer architectures, a condition estimate computable using the matrix sign function, and iterative algorithms for solving the linear Lyapunov equation. Finally, implementation of the algorithms as high quality, reliable mathematical software is proposed, in order to make the results of the research available for use by the control systems community. The solution of algebraic Riccati equations is a fundamental computational problem in control engineering and is essential for the application of many modern control techniques.

提出了求解超大型矩阵代数Riccati方程的并行算法和向量算法的发展。要使用的方法强调使用计算内核，如BLAS3，这些内核可在各种并行计算机上使用。这种方法将使算法可移植到许多先进的科学计算机上。许多研究都是基于矩阵符号函数算法，这是一种迭代方法，已被证明在某类多处理器上运行良好。研究课题包括易于并行化的“富含乘法”的算法，用于几种不同高级计算机体系结构的并行和向量算法，一个可用矩阵符号函数计算的条件估计，以及解线性Lyapunov方程的迭代算法。最后，提出了将算法实现为高质量、可靠的数学软件，以便将研究结果提供给控制系统社区使用。代数Riccati方程的求解是控制工程中的一个基本计算问题，是控制工程中的一个重要问题。许多现代控制技术的应用。