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Downward continuation of airborne geomagnetic data based on two iterative regularization methods in the frequency domain 被引量:8
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作者 Liu Xiaogang Li Yingchun +1 位作者 Xiao Yun Guan Bin 《Geodesy and Geodynamics》 2015年第1期34-40,共7页
Downward continuation is a key step in processing airborne geomagnetic data. However,downward continuation is a typically ill-posed problem because its computation is unstable; thus, regularization methods are needed ... Downward continuation is a key step in processing airborne geomagnetic data. However,downward continuation is a typically ill-posed problem because its computation is unstable; thus, regularization methods are needed to realize effective continuation. According to the Poisson integral plane approximate relationship between observation and continuation data, the computation formulae combined with the fast Fourier transform(FFT)algorithm are transformed to a frequency domain for accelerating the computational speed. The iterative Tikhonov regularization method and the iterative Landweber regularization method are used in this paper to overcome instability and improve the precision of the results. The availability of these two iterative regularization methods in the frequency domain is validated by simulated geomagnetic data, and the continuation results show good precision. 展开更多
关键词 Downward continuation regularization parameter Iterative tikhonov regularization method Iterative Landweber regularization metho
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An iterative algorithm for solving ill-conditioned linear least squares problems 被引量:8
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作者 Deng Xingsheng Yin Liangbo +1 位作者 Peng Sichun Ding Meiqing 《Geodesy and Geodynamics》 2015年第6期453-459,共7页
Linear Least Squares(LLS) problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics... Linear Least Squares(LLS) problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm(SAIA) is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy. 展开更多
关键词 Severe ill-conditioned matrix Linear least squares problems Self-adaptive Iterative scheme Cholesky decomposition regularization parameter tikhonov solution Truncated SVD solution
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