Mathematical Sciences: Completely Integrable Hamiltonian Systems

数学科学：完全可积哈密顿系统

• 批准号: 8704097
• 负责人: Luen-Chau Li
• 金额: $ 4.96万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-09-01 至 1991-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8704097&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Completely; Integrable; Hamiltonian; Mathematical; Sciences; Completely; Integrable; Hamiltonian

Professor Li will investigate the relationship between eigenvalue algorithms and integrable Hamiltonian systems. Together with his collaborators, he has proved the complete integrablity of the Toda (QL) flows on orbits through generic symmetric matrices. Further research will focus on the Hamiltonian structure and the question of complete integrability for the LU flows, the Chloesky flows and the extension of the Toda flows to nonsymmetric matrices. Professor Li will also investigate two related classes of flows which are important derivates of the Toda flows and are linkeed to the QL family of algorithms, such as QZ and SVD. These flows are not isospectral, but one of them preserves singular values of matrices, while the other preserves eigenvalues of matrix pencils. This research is part of theoretical efforts aimed at a better understanding of computational methods related to matrix eigenvalue problems.

Li教授将调查特征值算法与可综合的哈密顿系统之间的关系。 他与他的合作者一起证明了TODA（QL）通过通用的对称矩阵在轨道上流动的完全整合性。 进一步的研究将集中于哈密顿的结构以及LU流，Chloesky流以及TODA流向非对称矩阵的完全集成性问题。 Li教授还将调查两个相关类别的流量，这是TODA流的重要派生，并将其属于QL的算法家族，例如QZ和SVD。 这些流不是同一光谱，而是其中一个保留了矩阵的奇异值，而另一个则保留了矩阵铅笔的特征值。 这项研究是旨在更好地理解与矩阵特征值问题有关的计算方法的理论努力的一部分。