The parameter iteration method was developed for solving the nonlinear problem in this paper. The results of several examples show that even the first iteration solution has very good accuracy.
For stabilized saddle-point problems, we apply the two iteration parameters idea for regularized Hermitian and skew-Hermitian splitting (RHSS) method and establish accelerated RHSS (ARHSS) iteration method. Theoretica...For stabilized saddle-point problems, we apply the two iteration parameters idea for regularized Hermitian and skew-Hermitian splitting (RHSS) method and establish accelerated RHSS (ARHSS) iteration method. Theoretical analysis shows that the ARHSS method converges unconditionally to the unique solution of the saddle point problem. Finally, we use a numerical example to confirm the effectiveness of the method.展开更多
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
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
Defect classification is the key task of a steel surface defect detection system.The current defect classification algorithms have not taken the feature noise into consideration.In order to reduce the adverse impact o...Defect classification is the key task of a steel surface defect detection system.The current defect classification algorithms have not taken the feature noise into consideration.In order to reduce the adverse impact of feature noise,an anti-noise multi-class classification method was proposed for steel surface defects.On the one hand,a novel anti-noise support vector hyper-spheres(ASVHs)classifier was formulated.For N types of defects,the ASVHs classifier built N hyper-spheres.These hyper-spheres were insensitive to feature and label noise.On the other hand,in order to reduce the costs of online time and storage space,the defect samples were pruned by support vector data description with parameter iteration adjustment strategy.In the end,the ASVHs classifier was built with sparse defect samples set and auxiliary information.Experimental results show that the novel multi-class classification method has high efficiency and accuracy for corrupted defect samples in steel surface.展开更多
文摘The parameter iteration method was developed for solving the nonlinear problem in this paper. The results of several examples show that even the first iteration solution has very good accuracy.
文摘For stabilized saddle-point problems, we apply the two iteration parameters idea for regularized Hermitian and skew-Hermitian splitting (RHSS) method and establish accelerated RHSS (ARHSS) iteration method. Theoretical analysis shows that the ARHSS method converges unconditionally to the unique solution of the saddle point problem. Finally, we use a numerical example to confirm the effectiveness of the method.
基金supported by the National Natural Science Foundation of China(41304022,41174026,41104047)the National 973 Foundation(61322201,2013CB733303)+1 种基金the Key laboratory Foundation of Geo-space Environment and Geodesy of the Ministry of Education(13-01-08)the Youth Innovation Foundation of High Resolution Earth Observation(GFZX04060103-5-12)
文摘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.
基金supported by Open Fund of Engineering Laboratory of Spatial Information Technology of Highway Geological Disaster Early Warning in Hunan Province(Changsha University of Science&Technology,kfj150602)Hunan Province Science and Technology Program Funded Projects,China(2015NK3035)+1 种基金the Land and Resources Department Scientific Research Project of Hunan Province,China(2013-27)the Education Department Scientific Research Project of Hunan Province,China(13C1011)
文摘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.
基金This work was supported by the National Natural Science Foundation of China(No.51674140)Natural Science Foundation of Liaoning Province,China(No.20180550067)+2 种基金Department of Education of Liaoning Province,China(Nos.2017LNQN11 and 2020LNZD06)University of Science and Technology Liaoning Talent Project Grants(No.601011507-20)University of Science and Technology Liaoning Team Building Grants(No.601013360-17).
文摘Defect classification is the key task of a steel surface defect detection system.The current defect classification algorithms have not taken the feature noise into consideration.In order to reduce the adverse impact of feature noise,an anti-noise multi-class classification method was proposed for steel surface defects.On the one hand,a novel anti-noise support vector hyper-spheres(ASVHs)classifier was formulated.For N types of defects,the ASVHs classifier built N hyper-spheres.These hyper-spheres were insensitive to feature and label noise.On the other hand,in order to reduce the costs of online time and storage space,the defect samples were pruned by support vector data description with parameter iteration adjustment strategy.In the end,the ASVHs classifier was built with sparse defect samples set and auxiliary information.Experimental results show that the novel multi-class classification method has high efficiency and accuracy for corrupted defect samples in steel surface.
