Analyzing & Improving Numerical Algorithms for Eigenproblems Using Singularity Theory and Riemannian Geometry

分析

• 批准号: 9501278
• 负责人: Alan Edelman
• 金额: $ 5.7万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501278&HistoricalAwards=false
• 关键词: Analyzing; & Improving; Numerical; Algorithms

9501278 Edelman This work is supported by a National Science Foundation Faculty Early Career Development Award. The research component will focus on the application of new geometrical ideas to analyze and improve numerical algorithms. Part of the program will involve the derivation and study of an optimization technique on the Grassman manifold suitable for solving the Kohn-Sham equations of the local density approximation to Schroedinger's equation used in condensed matter physics and in materials science. The second part of the program involves the application of singularity theory to analyze and explain the behavior of certain numerical algorithms widely used in eigensystem analysis and systems and control. The education component will include further development of a new course in scientific computing at the Massachusetts Institute of Technology. Computers with a projection system will be used in undergraduate and graduate courses in numerical analysis and applied mathematics in order to bring new insights into the material. Mentoring and training of new researchers will also take place and will integrate the research and educational activities. The National Science Foundation strongly encourages the early development of academic faculty as both educators and researchers. The Faculty Early Career Development (CAREER) Program is a Foundation- wide program that provides for the support of junior faculty within the context of their overall career development. It combines in a single program the support of quality research and education in the broadest sense and the full participation of those traditionally underrepresented in science and engineering. This program enhances and emphasizes the importance the Foundation places on the development of full, balanced academic careers which include both research and education.

小行星9501278 这项工作得到了美国国家科学基金会的支持， 职业发展奖。 研究部分将侧重于 应用新的几何思想分析和改进数值计算 算法 该计划的一部分将涉及推导和研究一个 Grassman流形上的优化技术，适用于求解 Schroedinger局域密度近似的Kohn-Sham方程 凝聚态物理学和材料科学中使用的方程。 的 该计划的第二部分涉及奇点理论的应用， 广泛分析和解释某些数值算法的行为 用于特征系统分析和系统与控制。 教育 这一部分将包括进一步开发一个新的科学课程， 在马萨诸塞州理工学院学习计算机。 计算机与 投影系统将用于本科和研究生课程， 数值分析和应用数学，以带来新的见解 到材料中。 指导和培训新的研究人员也将采取 地方，并将整合研究和教育活动。 美国国家科学基金会强烈鼓励早期 发展学术教师作为教育工作者和研究人员。 的 教师早期职业发展（CAREER）计划是一个基金会范围内的计划，为初级教师提供支持， 在整体职业发展的背景下。 它结合在一个单一的 计划在最广泛的意义上支持高质量的研究和教育 以及传统上在科学领域代表性不足的人的充分参与 与工程学 该计划增强并强调了 基金会致力于发展全面、均衡的学术 包括研究和教育的职业。