A Newton Type Iterative Method for Heat-Conduction Inverse Problems
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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．
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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
Abstract: An inverse problem for identification of the coefficient in heat-conduction equation is considered. 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. -
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