| 大地测量与地球物理中病态性问题的正则化迭代解法 |
| |
| 引用本文： | 顾勇为,归庆明,张璇,魏萌.大地测量与地球物理中病态性问题的正则化迭代解法[J].测绘学报,2014,43(4):331. |
| |
| 作者姓名： | 顾勇为 归庆明 张璇 魏萌 |
| |
| 作者单位： | 1. 信息工程大学;
2. 信息工程大学理学院;
3. 中船重工集团第713研究所 |
| |
| 基金项目： | 国家自然科学基金(41174005;40974009);郑州市科技计划(0910SGYG21198) |
| |
| 摘 要： | 大地测量与地球物理中需要求解的大规模超定线性方程组常常具有病态性，在使用共轭梯度法求解时必须克服病态性的危害影响，本文对此进行了研究，利用正则化思想改进共轭梯度解法，提出了基于条件数控制的正则化迭代解法。首先通过构造干扰源向量，推导了与法方程同解且病态性大为减弱的新的解算方程，然后用共轭梯度迭代法对新方程求解，最后通过航空重力向下延拓等数值试验验证了新解法的有效性，并且将其与LS、CG、Tikhonov等方法比较，结果表明新方法的精度最高。
|
| 关 键 词： | 病态性 正则化方法 条件数 干扰源向量 迭代 |
| 收稿时间： | 2012-10-31 |
| 修稿时间： | 2013-01-30 |
Iterative Solution of Regularization Based on Controlling Condition Number |
| |
| Abstract: | In geodesy and geophysics, many large-scale over-determined linear equations need to be solved which are often ill-conditioned. When the conjugate gradient method is used, their ill-conditioned effects to the solutions must be overcome, which is studied in this paper. By regularization ideas, the conjugate gradient method is improved; the regularization iterative solution based on controlling condition number is put forward. Firstly by constructing the interference source vector, a new equation is derived with ill-condition diminished greatly, which has the same solution to the original normal equation. Then the new equation is solved by conjugate gradient method. Finally the effectiveness of the new method is verified by some numerical experiments of airborne gravity downward to the earth surface. In the numerical experiments the new method is compared with LS, CG and Tikhonov methods, and its accuracy is the highest. |
| |
| Keywords: | |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《测绘学报》浏览原始摘要信息 |
| 点击此处可从《测绘学报》下载免费的PDF全文 |
|
