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

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.

李教授将研究特征值算法与可积哈密顿系统之间的关系。 他与他的合作者一起，通过通用对称矩阵证明了 Toda (QL) 流在轨道上的完全可积性。 进一步的研究将集中于哈密顿结构以及 LU 流、Chloesky 流和 Toda 流向非对称矩阵的扩展的完全可积问题。 李教授还将研究两类相关的流，它们是 Toda 流的重要衍生物，并与 QL 系列算法相关，例如 QZ 和 SVD。 这些流不是等谱的，但其中一个保留矩阵的奇异值，而另一个保留矩阵铅笔的特征值。 这项研究是理论工作的一部分，旨在更好地理解与矩阵特征值问题相关的计算方法。