Mathematical Sciences: Inverse Eigenvalue Problems

数学科学：反特征值问题

• 批准号: 9422280
• 负责人: Moody Chu
• 金额: $ 7.5万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-05-15 至 1999-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9422280&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Inverse; Eigenvalue; Problems

9422280 Chu PRIVATE This research is concerned with inverse eigenvalue problems. Both the theory and the practice of constructing a physical model, described mathematically in the form of a matrix, from prescribed spectral data will be investigated. This proposal continues and extends previous studies. In particular, a dynamical system for each inverse eigenvalue problem will be formulated to ensure that a specific task is taking place continuously. The dynamics will then be explored using computer experiments, high resolution graphics and symbolic manipulation, in conjunction with analysis. This study should lead to fundamental advances in the understanding of inverse eigenvalue problems. This project is expected to find important applications ranging from new development of numerical algorithms to theoretical solutions of difficult problems. Since inverse eigenvalue problems arise from a wide variety of disciplines, the resulting technology would have impact on a number of scientific and engineering fields. Inverse eigenvalue problems arise in many important applications, including control design, vibration isolation, system identification, exploration and remote sensing, and signal processing. A significant common phenomenon in all these areas of application is that the physical parameter of a certain system is to be reconstructed from knowledge or expectation of its dynamical behavior, in particular its natural frequencies and/or normal modes. The advances obtained from this proposed work will contribute to the understanding of issues that arise in several strategic areas, particularly in the areas of global change, manufacturing, transportation, and environmental monitoring.

9422280 CHU私人这项研究与特征值问题有关。从规定的光谱数据中以矩阵形式描述的物理模型的理论和实践都将得到研究。 该建议继续并扩展了以前的研究。 特别是，将制定一个针对每个逆特征值问题的动态系统，以确保连续执行特定任务。 然后，将使用计算机实验，高分辨率图形和符号操作来探索动力学，并结合分析。这项研究应导致理解逆值问题的基本进展。 预计该项目将找到重要的应用程序，从数值算法的新开发到困难问题的理论解决方案。 由于特征值问题是由多种学科引起的，因此所得技术将对许多科学和工程领域产生影响。 在许多重要应用中出现了逆特征值问题，包括控制设计，振动隔离，系统识别，探索和遥感以及信号处理。 在所有这些应用领域中，一个重要的共同现象是，某个系统的物理参数应从对其动力学行为的知识或期望重建，尤其是其固有频率和/或正常模式。 从这项拟议的工作中获得的进步将有助于理解在几个战略领域中出现的问题，尤其是在全球变化，制造，运输和环境监测领域。