| 全变差正则化方法对一类热传导反问题的应用 |
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| 引用本文： | 田俊改,肖庭延.全变差正则化方法对一类热传导反问题的应用[J].中国民航学院学报,2004,22(3):55-59. |
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| 作者姓名： | 田俊改 肖庭延 |
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| 作者单位： | 中国民用航空学院理学院 天津300300
(田俊改)，河北工业大学理学院 天津300130(肖庭延) |
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| 摘 要： | 热传导终端反问题是典型的不适定问题,应用基于全变差的正则化方法来获得它的稳定数值解,将近似解的求解范围由连续函数空间扩大到了有界变差函数空间,并将固定点迭代法用于求解非线性的Euler方程,并进行了理论分析和数值实验。结果表明:该方法与算法具有高效稳定全局收敛等优点。
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| 关 键 词： | 热传导终端反问题 不适定问题 全变差 正则化方法 固定点迭代法 |
| 文章编号： | 1001-5000(2004)03-0055-05 |
| 修稿时间： | 2004年3月31日 |
Application of Total Variation-based Regularization to Inverse Problem of a Kind of Heat Equation |
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| TIAN Jun-gai,XIAO Ting-yan.Application of Total Variation-based Regularization to Inverse Problem of a Kind of Heat Equation[J].Journal of Civil Aviation University of China,2004,22(3):55-59. |
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| Authors: | TIAN Jun-gai XIAO Ting-yan |
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| Institution: | TIAN Jun-gai1,XIAO Ting-yan2 |
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| Abstract: | Sideways heat equation is a typical ill-posed problem.Variation-based Regularization is used to gain stable numerical solution of the kind of heat equation.This method extends the solution space to the space of bounded variation functions.Fixed-point iteration is used to solve the difficulty raised from nonlinear of Euler equation.Theoretical analysis and numerical test indicate that the new method and algorithems possess the advantages of high-efficiency,good numerical stability, global convergence and so on. |
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| Keywords: | sideways heat equation ill-posed problem total variation regularization fixed-point iteration |
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