Kernel-based Approximation Methods for Ill-posed Problems

发布者:系统管理员发布时间:2011-04-08浏览次数:2101

报告题目: Kernel-based Approximation Methods for Ill-posed Problems
报 告 人: Benny Hon
  香港城市大学数学系
报告时间: 4月18号下午14:00-15:00
报告地点: 数学系九龙湖第一报告厅
相关介绍: In this talk we present the recent development of meshless computational methods
based on the use of kernel-based functions for solving various ill-posed problems. 
Properties of some special kernels such  as harmonic kernels; kernels from the
construction of fundamental and particular solutions; Greens functions; and radial
basis functions will be discussed.  As an illustration, the recent work in using the
method of fundamental solutions  combined  with  the Tikhonov  regularization
technique to solve Cauchy problems and inverse heat conduction/source identification
problems  will  be  demonstrated.   The main idea is to approximate the unknown
solution by a linear combination of fundamental solutions whose singularities are
located outside the solution domain.  The L-curve method for searching an optimal
regularization parameter is then adopt to obtain stable solution from measured data
with noises.