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.
