| 一种新Tikhonov正则化方法 |
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| 引用本文： | 郭淑妹,李豪,郭杰.一种新Tikhonov正则化方法[J].西南师范大学学报(自然科学版),2018,43(6):46-51. |
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| 作者姓名： | 郭淑妹 李豪 郭杰 |
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| 作者单位： | 信息工程大学基础部 |
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| 基金项目： | 国家自然科学基金项目（41174005，40974009）. |
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| 摘 要： | 由矩阵变换得到一种新的Tikhonov正则化方法,是截断奇异值法和Tikhonov正则化方法的结合.通过3种正则化方法的滤波因子,对3种方法进行概括.并通过大地测量中的控制网平差、重力向下延拓的实例对3种方法进行比较,得出新方法在减小解均方误差、提高未知数的精度等方面具有一定的有效性.
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| 关 键 词： | 病态性 奇异值分解 Tikhonov正则化 滤波因子 |
| 收稿时间： | 2018/3/10 0:00:00 |
A New Tikhonov Regularization Method |
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| Guo Shu-mei,LI Hao,GUO Jie.A New Tikhonov Regularization Method[J].Journal of Southwest China Normal University(Natural Science),2018,43(6):46-51. |
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| Authors: | Guo Shu-mei LI Hao GUO Jie |
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| Institution: | Department of Basic, Information Engineering University, Zhengzhou 450001, China |
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| Abstract: | A new Tikhonov regularization method is obtained by Matrix transformation.The new Tikhonov regularization method is combined with the truncation singular value method and the Tikhonov regularization method. The three methods are compared by their filtering factors.The three methods are verified by the control network adjustment and gravity downward extension in Geodesy, and the results show that the new method is effective in reducing the mean square error and improving the accuracy of estimation. |
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| Keywords: | ill-conditioned singular value decomposition Tikhonov regularization filter factors |
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