An immediate and the most straight implementation of inverse eigenvalue problems is to consider the construction of a vibration system from its observed or desirable dynamical behavior while respecting some inherent feasibility constraints. Considerable efforts have been taken to derive theory and numerical methods for solving inverse eigenvalue problems, but techniques developed thus far can handle the inverse problems only on a case by case basis. Our goals are to discover an efficient and reliable programming capable of handling all kinds of structures and to derive theoretical approaches for solving these problems. The second topic, low rank approximations, has become increasingly important and ubiquitous in this era of information. Its goal is to analyze and uncover the embedded information in a given data. Generally, there is no unified approach because the technique often is data type dependent. Our work is to study and propose new factorization techniques for different types of data.
I am looking for students who have the character of diligence and the concept of working practically and are interested in working on inverse problems and optimization problems. Students with a range of backgrounds are welcomed and it is much possible to tailor research problems with respect to a student's capacity and interest. If you are one of the students who are interested in working with me, please contact me via email or just come by my office.