报告题目:Study of Effective Condition Number

报告人：黄宏财 教授

报告时间：上午9:30—10:30

报告地点：广知楼 A 楼 204

报告题目：Study of Effective Condition Number

报告时间：2019.06.18  (周二) 上午9:30—10:30

报告地点：广知楼 A 楼 204 

报告人：黄宏财 教授

摘要：  For solving the linear algebraic equations Ax = b with the symmetric and positive definite matrix A, the traditional condition number in the 2-norm is defined by Cond = lambda_1/lambda_n , where lambda_1 and lambda_n are the maximal and the minimal eigenvalues of the matrix A, respectively. The condition number is used to provide the bounds of the relative errors from the perturbation of both A and b. Such a Cond can only be reached by the worst situation of all rounding errors and all b. For the given b the true relative errors may be smaller, or even much smaller than the Cond, which is called the effective condition number in Chan and Foulser (1988) and Christiansen and Hansen(1994). The condition number originated from Wilkinson (1963), and it has been using for stability analysis. In this study, the new effective condition number, Cond eff = norm(b)/lambda_n/norm(x), is proposed to explore the stability of numerical partial differential equations. Since the effective condition number is smaller, and even much smaller than the condition number, the effective condition number may provide a sharp estimation of stability analysis. In fact, the effective condition number was first studied in Rice (1981), but is not noticeable in the community of linear algebra. However, the effective condition number is remarkably advantageous over the traditional condition number for numerical partial differential equations. The materials of this talk are taken from the monograph [Z.C. Li, H.T. Huang, Y. Wei, A.H.-D Cheng, Effective condition number for Numerical Partial Differential Equations (Second Edition), Science Press, Beijing, 2015.]

本报告为综述性介绍报告，欢迎广大本科生、研究生前来参加。

报告人简介：

黄宏财，台湾义守大学教授。2003年博士毕业于台湾中山大学，师从李子才教授，研究方向为数值分析和科学计算。在Engineering Analysis with Boundary Elements, Applied Numerical Mathematics, J. Computational and Applied Mathematics, Numerical Linear Algebra with Applications等国际重要期刊发表论文四十余篇，合作完成三本专著。多次参加国际会议并给出会议报告或者海报。