| 求解热源识别问题的修正吉洪诺夫正则化方法 |
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| 引用本文： | 赵振宇,由雷. 求解热源识别问题的修正吉洪诺夫正则化方法[J]. 数学物理学报(A辑), 2014, 34(1): 186-192 |
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| 作者姓名： | 赵振宇 由雷 |
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| 作者单位： | 广东海洋大学理学院 广东 湛江 524088 |
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| 基金项目： | 国家自然科学基金(11201085)资助. |
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| 摘 要： | 该文研究了一个热源识别问题,通过引入修正吉洪诺夫方法来处理问题的不适定性,在一种先验和一种后验参数选取准则下,分别获得了问题的误差估计.数值例子进一步验证了方法的有效性和稳定性.
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| 关 键 词： | 不适定问题 未知源 热方程 正则化方法 偏差原理 |
| 收稿时间： | 2012-10-12 |
| 修稿时间： | 2013-09-30 |
A Modified Tikhonov Regularization Method for Identifying an Unknown Source in the Heat Equation |
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| ZHAO Zhen-Yu,YOU Lei. A Modified Tikhonov Regularization Method for Identifying an Unknown Source in the Heat Equation[J]. Acta Mathematica Scientia, 2014, 34(1): 186-192 |
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| Authors: | ZHAO Zhen-Yu YOU Lei |
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| Affiliation: | College of Science, Guangdong Ocean University, Guangdong Zhanjiang |524088 |
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| Abstract: | In this paper, we consider the problem for determining the unknown source in the heat equation. A modified Tikhonov regularization method is presented to deal with the illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical tests show that the proposed method is effective and stable. |
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| Keywords: | Ill-posed problemzz Unknown sourcezz Heat equationzz Regularization methodzz Discrepancy principlezz Hilbert scaleszz |
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