Xiaowen Chang

报告人：  Professor Xiao-Wen Chang (常晓文教授)      
                   School of Computer Science, McGill University, Canada

报告题目： Backward Perturbation Analysis for  Scaled Total Least Squares Problems

时间地点： 2008年12月28日下午3点， 蒙民伟楼311室

常晓文简介：

常晓文分别于1986年、1989年在南京大学计算数学专业获得学士、硕士学位，后到加拿大McGill 大学计算机科学学院攻读博士研究生，师从国际著名数值分析学家C.C.Paige教授，并获得博士学位。现为加拿大McGill 大学计算机科学学院教授，常晓文教授在SIAM系列刊物、IEEE Transactions刊物、BIT等重要期刊发表文章40多篇，是国际计算科学与工程、数值分析领域的知名学者。常晓文教授担任他们系的研究生主任（Graduate Director ），如对加拿大McGill 大学计算机科学学院读研究生感兴趣的计算机系、数学系和相关学科的同学，欢迎到时和常晓文教授交流。

报告摘要
Given an approximate solution to a problem, the aim of backward perturbation analysis is to find a perturbation in the data with minimum size (referred to as the minimal backward error) such that the approximate solution is an exact solution of the perturbed problem. The results of a backward perturbation analysis can be used to determine if a computed solution is a numerically stable solution and to design effective stopping criteria for solving large sparse problems.

This talk is concerned with backward perturbation analysis of the scaled total least squares (STLS) problems. We will present a formula for what we call an "extended" minimal backward error, which is at worst a lower bound on the minimal backward error. From this formula, we can obtain the minimal backward error for the ordinary LS problem and the extended minimal backward error for the data LS problem. When the given approximate solution is a good enough approximation to the exact solution of the STLS problem (which is the aim in practice), the extended minimal backward error is the ac
tual the minimal backward error. Since it is computationally expensive to compute the extended minimal backward error directly, we derive a lower bound on it and an asymptotic estimate for it, both of which can be evaluated less expensively. Simulation results show that for reasonable approximate solutions the lower bound has the same order as the extended minimal backward error, and the asymptotic estimate is an excellent approximation to the extended minimal backward error.This is joint work with Chris Paige and David Titley-Peloquin.