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| 病态问题解算的直接正则化方法比较 | |
| 引用本文： | 范千,方绪华,范娟.病态问题解算的直接正则化方法比较[J].贵州大学学报(自然科学版),2011,28(4):29-32. |
| 作者姓名： | 范千 方绪华 范娟 |
| 作者单位： | 1. 福州大学土木工程学院,福建福州350108;江西省数字国土重点实验室,江西抚州344000 2. 福州大学土木工程学院,福建福州,350108 3. 安徽省无为六洲中学,安徽巢湖,238300 |
| 基金项目： | 江西省数字国土重点实验室开放基金资助项目(DLLJ201102); 福建省教育厅科技资助项目(JA10045); 福建省自然科学基金资助项目(2009J05102); 福州大学科研启动基金资助项目(022355) |
| 摘 要： | 为了解算病态问题,需正确选择适合的正则化方法,为此分析了截断奇异值法和Tikhonov正则化方法的异同点.在此基础上,阐述了L曲线法和GCV法确定最优正则化参数的基本原理.通过数值算例分析表明:截断奇异值法和Tikhonov法可以有效消除观测方程的病态性；利用L曲线法和GCV法不仅可以对Tikhonov方法中的连续正则... |
| 关 键 词： | 正则化方法 截断奇异值法 Tikhonov法 L曲线 GCV |
Comparison of Direct Regularization Methods of Ill-conditioned Problems Solution |
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| FAN Qian,FANG Xu-hua,FAN Juan.Comparison of Direct Regularization Methods of Ill-conditioned Problems Solution[J].Journal of Guizhou University(Natural Science),2011,28(4):29-32. | |
| Authors: | FAN Qian FANG Xu-hua FAN Juan |
| Institution: | FAN Qian1,2,FANG Xu-hua1,FAN Juan3 (1.College of Civil Engineering,Fuzhou University,Fuzhou 350108,China,2.Digital Land Key Laboratory of Jiangxi Province,Fuzhou 344000,3.Wu Wei Liu Zhou High School of Anhui Province,Chaohu 238300,China) |
| Abstract: | In order to resolve ill-conditioned problems,suitable regularization methods are needed to choose correctly.The characteristics of truncated singular value decomposition(TSVD) method and Tikhonov regularization method are discussed respectively.On the basis,L-curve method and generalized cross validation(GCV) method are both employed to attain the optimal regularization parameters.Numerical results show that TSVD method and Tikhonov method can eliminate ill-condition of observation equation effectively.Thro... |
| Keywords: | regularization method truncated singular value decomposition method Tikhonov method L-curve GCV |
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