| 一维波动方程反问题的不适定性及正则化分析 |
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| 引用本文： | 王宝娥.一维波动方程反问题的不适定性及正则化分析[J].陕西理工学院学报(自然科学版),2005,21(4):89-91. |
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| 作者姓名： | 王宝娥 |
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| 作者单位： | 西安理工大学,理学院,陕西,西安,710048 |
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| 摘 要： | 基于一维波动方程反问题的数学模型,应用奇异值分解分析算子方程的不适定性。讨论了正则解的求解方法,并利用Tikhonov正则化方法克服反问题的不适定性。最后根据正则化参数的确定原则,采用精度高和适应性更好的遗传算法确定最优正则化参数。
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| 关 键 词： | 波动方程 反问题 奇异值分解 Tikhonov正则化 |
| 文章编号： | 1673-2944(2005)04-0089-03 |
| 收稿时间： | 2005-08-27 |
| 修稿时间： | 2005年8月27日 |
Ill-posed nature and regularization of inverse problem for one dimensional wave equation |
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| WANG Bao-e.Ill-posed nature and regularization of inverse problem for one dimensional wave equation[J].Journal of Shananxi University of Technology:Natural Science Edition,2005,21(4):89-91. |
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| Authors: | WANG Bao-e |
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| Abstract: | According to inverse problem mathematical model of one dimensional wave equation,the singular value decomposition(SVD) technique is applied to analyze the characteristics of inversion equations.The method of solving problem for regularization answer is discussed and Tikhonov regularization method is applied to overcome the ill-posed nature of inverse problem.In the end,the genetic algorithms which has better precision and efficiency is adopted for finding the optimal regularization parameter based on the solution rule of regularization parameter. |
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| Keywords: | wave equation inverse problem singular value decomposition(SVD) tikhonov regularization |
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