演講者：林敏雄先生

單　位：北卡羅來納州立大學數學系

日　期：2010年2月24日　PM 16:00

地　點：國立高雄大學理學院408室

講　題：Inverse Problem of Matrix Data Reconstruction 

摘　要：

Motivation: The study of Inverse problems is intended to discover the desired characteristics embedded in the original systems. Applications include vibration analysis of structural systems,  vibroacoustics, fluid mechanics, model updating problems, signal processing, association analysis, classification analysis, imaging techniques, and so on and so forth. This talk will focus on two topics: (1)quadratic inverse eigenvalue problems (2)the low rank approximation of matrices. 

Results:

· For quadratic inverse eigenvalue problems, conventional methods can only handle problems on a case-by-case basis. In this talk, we will explain how to apply two renowned methods: semi-definite programming and the QR decomposition, for solving problems with all kinds of structured dynamical systems.

· For low rank factorization problems (LRF), the general purpose is to rephrase the original difficult problem through a series of easier subproblems. The traditional approach to the LRF is to express the matrix as the product of two or more factors and then perform suitable truncations. During this talk, we will discuss how to apply the Wedderburn rank-one reduction formula, known to unify almost all matrix decompositions in numerical linear algebra, to break down the matrix into rank-one matrices, how to handle nonnegative matrix data by using the powerful Hanh-Banach theory, and how to extract the characteristics of some given discrete data. We will apply our methods to some practical data and offer numerical analysis of the results obtained.