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大地测量与地球物理中病态性问题的正则化迭代解法 被引量:23
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作者 顾勇为 归庆明 +1 位作者 张璇 魏萌 《测绘学报》 EI CSCD 北大核心 2014年第4期331-336,共6页
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,本文利用正则化思想改进了共轭梯度解法。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... 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,本文利用正则化思想改进了共轭梯度解法。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,并且将其与最小二乘法、共轭梯度法、Tikhonov等方法比较,结果表明新方法的精度较高。 展开更多
关键词 病态性 正则化方法 条件数 干扰源向量 迭代
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Iterative Solution of Regularization to Ill-conditioned Problems in Geodesy and Geophysics 被引量:4
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作者 Yongwei GU Qingming GUI +1 位作者 Xuan ZHANG Songhui HAN 《Journal of Geodesy and Geoinformation Science》 2019年第1期59-65,共7页
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-conditioning effects to the solutions ... 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-conditioning effects to the solutions must be overcome,which is studied in this paper.Through the regularization ideas,the conjugate gradient method is improved,and 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. 展开更多
关键词 ILL-CONDITION REGULARIZATION condition number interference source vector ITERATION
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