| A Newton type iterative method for heat-conduction inverse problems |
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| 作者姓名： | 贺国强 孟泽红 |
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| 作者单位： | Department of Mathematics Shanghai University，Shanghai 200444，P. R. China，Department of Mathematics，Shanghai University，Shanghai 200444，P. R. China |
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| 摘 要： | 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 are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is 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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| 收稿时间： | 28 August 2006 |
A Newton type iterative method for heat-conduction inverse problems |
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| HE Guo-qiang,MENG Ze-hong.A Newton type iterative method for heat-conduction inverse problems[J].Applied Mathematics and Mechanics(English Edition),2007,28(4):531-539. |
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| Authors: | HE Guo-qiang MENG Ze-hong |
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| Institution: | Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China |
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| 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 are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is 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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| Keywords: | inverse problems nonlinear ill-posed operator equations Newton type method implicit iterative method iteration stopping rule |
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