Mathematical Sciences: Inverse Eigenvalue Problems

9422280楚私人 本研究是关于逆特征值问题。理论和 构造物理模型的实践，以数学形式描述， 矩阵，从规定的光谱数据将进行研究。 这项建议继续下去， 扩展了以前的研究。 特别地，每个逆特征值的动力系统 问题将被制定，以确保一个特定的任务正在不断发生。 的 然后将使用计算机实验，高分辨率图形和 符号操作，结合分析。这项研究将导致基本的 在逆特征值问题的理解的进展。 该项目预计将 发现从数值算法的新发展到 困难问题的理论解决方案。 由于逆特征值问题产生于 广泛的学科，由此产生的技术将对一些 科学和工程领域。 逆特征值问题出现在许多重要的应用中，包括控制 设计、隔振、系统识别、勘探和遥感，以及 信号处理 在所有这些应用领域中的一个重要的共同现象是 某个系统的物理参数将根据知识重建，或者 其动态行为的预期，特别是其固有频率和/或正常 modes. 从这项拟议工作中获得的进展将有助于 对若干战略领域出现的问题的理解，特别是 全球变化、制造、运输和环境监测。

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.