1 报告题目：On Some Hidden Markov Models and Their Applications
报告人：香港大学数学系 Ching Wai-Ki 教授
摘要：Hidden Markov Models (HMMs) are widely used in science, engineering and many other areas. In a HMM, there are two types of states: hidden states and observable states. Here we study a HMM via the framework of classical Markov chain model. Simple estimation method for the transition probabilities among the hidden states will be discussed. We then apply the model to customer classification and credit default modeling. Numerical examples are given to illustrate the usefulness of the model by using a real-world data set.
2 报告题目：An Arnoldi (M,W,G) Method for GE problems
3 报告题目：Doubling Algorithm for Solving Palindromic Quadratic Eigenvalue Problems Arising in Fast Trains A Structure-Preserving
报告人：Wen-Wei Lin (林文伟)教授，National Taiwan University
摘 要：We first introduce a finite element model for fast trains and derived the associated palindromic quadratic eigenvalue problems as well as the nonlinear matrix equation (NME). We present a generalization of Bendixson’s Theorem to bounded linear operators in infinite-dimensional Hilbert spaces and show the existence of the stabilizing complex symmetric solution of the nonlinear matrix equation. We then develop a structure-preserving doubling algorithm (SDA) for the computation of the stabilizing solution. Numerical results show that the SDA algorithm has fast convergence and solves NMEs efficiently and accurately.
4 报告题目：LEAST SQUARES PROBLEMS IN COORDINATE METROLOGY
报告人：Prof. Walter Gander，Computer Science Department of ETH ?xml:namespace>
摘要：In coordinate metrology, approximated geometrical objects are computed by least squares to fit to measured points. Coordinate metrology is part of measurement science. It is used in computer-aided inspection in manufacturing. In manufacturing a workpiece is fabricated according to plans which involve a mathematical description of the object. Coordinate metrology is the inverse process: a workpiece is measured by some coordinate measuring machine and a mathematical model is computed from the measured points by some least square approximation. We show in this talk some typical problems and describe algorithms for the solution.
5 报告题目：Variational Models in Image Processing
报告人：Michael Ng 教授, 香港浸会大学数学系
摘要：In this talk, I present some variational models in image processing for deblurring, illumination and stitching. Both theoretical and experimental results are presented to illustrate the models and the applications.
6 报告题目：Numerical Solutions of Coupled Nonlinear Schrodinger Equations by Orthogonal Spline Collocation Method
报 告 人：金小庆教授，澳门大学数学系
摘要：In this paper, we present the use of the orthogonal spline collocation method for the semi-discretization scheme of the one-dimensional coupled nonlinear SchrÄodinger equations. This method uses the Hermite basis functions, by which physical quantities are approximated with their values and derivatives associated with Gaussian points. The convergence rate with order O(h^4 + \tau^2) and stability of the scheme are proved. Conservation properties are shown in both theory and practice. Extensive numerical experiments are presented to validate the numerical study under consideration.