求解热传导反问题的一种正则化Newton型迭代法  

A Newton Type Iterative Method for Heat-Conduction Inverse Problems

作　　者：贺国强[1] 孟泽红[1] 

机构地区：[1]上海大学数学系,上海200444

出　　处：《应用数学和力学》2007年第4期479-486,共8页Applied Mathematics and Mechanics

摘　　要：讨论热传导方程求解系数的一个反问题.把问题归结为一个非线性不适定的算子方程后,考虑该方程的Newton型迭代方法.对线性化后的Newton方程用隐式迭代法求解,关键的一步是引入了一种新的更合理的确定(内)迭代步数的后验准则.对新方法及对照的Tikhonov方法和Bakushiskii方法进行了数值实验,结果显示了新方法具有明显的优越性.An inverse problem for identification of the coefficient in heat-conduction equation is con- sidered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods were considered. The implicit iterative method was applied to the linearized Newton equation, and the key step in the process was that a new reasonable a posteriori stopping rule for the inner iteration was presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given. And these results show the obvious advantages of the new method over the other ones.

关 键 词：反问题 非线性不适定算子方程 Newton型方法 隐式迭代法 迭代终止准则 

分 类 号：O241[理学—计算数学]