Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate o...Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated.展开更多
In this paper, the Galerkin projection method is used for solving the semi Sylvester equation. Firstly the semi Sylvester equation is reduced to the multiple linear systems. To apply the Galerkin projection method, so...In this paper, the Galerkin projection method is used for solving the semi Sylvester equation. Firstly the semi Sylvester equation is reduced to the multiple linear systems. To apply the Galerkin projection method, some propositions are presented. The presented scheme is compared with the L-GL-LSQR algorithm in point of view CPU-time and iteration number. Finally, some numerical experiments are presented to show that the efficiency of the new scheme.展开更多
How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linea...How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms.We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system.Through the maximal orthogonal projection concept,to minimize a merit function within a selected interval of splitting parameters,the optimal parameters can be quickly determined.In each step,a linear system is solved by the Gaussian elimination method,and the whole iteration procedure is convergent very fast.Several numerical tests show the high performance of the optimal split-linearization iterative method(OSLIM).展开更多
A robust self-calibration method is presented, which can efficiently discard the outliers based on a Weighted Iteration Method (WIM). The method is an iterative process in which the projective reconstruction is obtain...A robust self-calibration method is presented, which can efficiently discard the outliers based on a Weighted Iteration Method (WIM). The method is an iterative process in which the projective reconstruction is obtained based on the weights of all the points, whereas the weights are defined in inverse proportion to the re- ciprocal of the re-projective errors. The weights of outliers trend to zero after several iterations, and the accu- rate projective reconstruction is determined. The location of the absolute conic and the camera intrinsic pa- rameters are obtained after the projective reconstruction. The theory and experiments with both simulate and real data demonstrate that the proposed method is very efficient and robust.展开更多
If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continu...If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continuation theory suggests that a finite-sized object can be uniquely determined by its frequency components in a very small neighborhood.Trying to obtain such an exact Taylor expansion is difficult.This paper proposes an iterative algorithm to extend the measured frequency components to unmeasured regions.Computer simulations show that the proposed algorithm converges very slowly,indicating that the problem is too ill-posed to be practically solvable using available methods.展开更多
In this paper, a new iterative solution method is proposed for solving multiple linear systems A(i)x(i)=b(i), for 1≤ i ≤ s, where the coefficient matrices A(i) and the right-hand sides b(i) are arbitrary in general....In this paper, a new iterative solution method is proposed for solving multiple linear systems A(i)x(i)=b(i), for 1≤ i ≤ s, where the coefficient matrices A(i) and the right-hand sides b(i) are arbitrary in general. The proposed method is based on the global least squares (GL-LSQR) method. A linear operator is defined to connect all the linear systems together. To approximate all numerical solutions of the multiple linear systems simultaneously, the GL-LSQR method is applied for the operator and the approximate solutions are obtained recursively. The presented method is compared with the well-known LSQR method. Finally, numerical experiments on test matrices are presented to show the efficiency of the new method.展开更多
In this paper, we introduce some new classes of the totally quasi-G-asymptotically nonexpansive mappings and the totally quasi-G-asymptotically nonexpansive semigroups. Then, with the generalized f-projection operator...In this paper, we introduce some new classes of the totally quasi-G-asymptotically nonexpansive mappings and the totally quasi-G-asymptotically nonexpansive semigroups. Then, with the generalized f-projection operator, we prove some strong convergence theorems of a new modified Halpern type hybrid iterative algorithm for the totally quasi-G-asymptotically nonexpansive semigroups in Banach space. The results presented in this paper extend and improve some corresponding ones by many others.展开更多
针对一般超分辨率算法无法在重建效果和运行速度上取得较好的平衡,结合结构相似性提出了一种具有保边性的迭代反投影算法(iterative back projection,IBP)的超分辨率算法。兼顾算法运行速度,在传统的IBP基础上添加各项异性扩散,使之具...针对一般超分辨率算法无法在重建效果和运行速度上取得较好的平衡,结合结构相似性提出了一种具有保边性的迭代反投影算法(iterative back projection,IBP)的超分辨率算法。兼顾算法运行速度,在传统的IBP基础上添加各项异性扩散,使之具有边缘增强和保边效果。为了结合更多的先验知识,将保边IBP和结构相似性结合在一起,使重建效果更加自然细腻。采用峰值信噪比和结构相似性度量评价算法效果。从实验结果数据可以看出,算法具有最高的PSNR值和SSIM值,其中SSIM的值最高可以达到0.95,非常接近于1。从实验结果图可以看出,算法的纹理保留的最好,图像更自然和准确。而且运行速度没有严重落后于传统IBP,具有很好的实用性。展开更多
Matrix completion is the extension of compressed sensing.In compressed sensing,we solve the underdetermined equations using sparsity prior of the unknown signals.However,in matrix completion,we solve the underdetermin...Matrix completion is the extension of compressed sensing.In compressed sensing,we solve the underdetermined equations using sparsity prior of the unknown signals.However,in matrix completion,we solve the underdetermined equations based on sparsity prior in singular values set of the unknown matrix,which also calls low-rank prior of the unknown matrix.This paper firstly introduces basic concept of matrix completion,analyses the matrix suitably used in matrix completion,and shows that such matrix should satisfy two conditions:low rank and incoherence property.Then the paper provides three reconstruction algorithms commonly used in matrix completion:singular value thresholding algorithm,singular value projection,and atomic decomposition for minimum rank approximation,puts forward their shortcoming to know the rank of original matrix.The Projected Gradient Descent based on Soft Thresholding(STPGD),proposed in this paper predicts the rank of unknown matrix using soft thresholding,and iteratives based on projected gradient descent,thus it could estimate the rank of unknown matrix exactly with low computational complexity,this is verified by numerical experiments.We also analyze the convergence and computational complexity of the STPGD algorithm,point out this algorithm is guaranteed to converge,and analyse the number of iterations needed to reach reconstruction error.Compared the computational complexity of the STPGD algorithm to other algorithms,we draw the conclusion that the STPGD algorithm not only reduces the computational complexity,but also improves the precision of the reconstruction solution.展开更多
文摘Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated.
文摘In this paper, the Galerkin projection method is used for solving the semi Sylvester equation. Firstly the semi Sylvester equation is reduced to the multiple linear systems. To apply the Galerkin projection method, some propositions are presented. The presented scheme is compared with the L-GL-LSQR algorithm in point of view CPU-time and iteration number. Finally, some numerical experiments are presented to show that the efficiency of the new scheme.
基金support provided by the Ministry of Science and Technology,Taiwan,ROC under Contract No.MOST 110-2221-E-019-044.
文摘How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms.We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system.Through the maximal orthogonal projection concept,to minimize a merit function within a selected interval of splitting parameters,the optimal parameters can be quickly determined.In each step,a linear system is solved by the Gaussian elimination method,and the whole iteration procedure is convergent very fast.Several numerical tests show the high performance of the optimal split-linearization iterative method(OSLIM).
基金Supported by the National Natural Science Foundation of China (No.60473119 and No.60372043).
文摘A robust self-calibration method is presented, which can efficiently discard the outliers based on a Weighted Iteration Method (WIM). The method is an iterative process in which the projective reconstruction is obtained based on the weights of all the points, whereas the weights are defined in inverse proportion to the re- ciprocal of the re-projective errors. The weights of outliers trend to zero after several iterations, and the accu- rate projective reconstruction is determined. The location of the absolute conic and the camera intrinsic pa- rameters are obtained after the projective reconstruction. The theory and experiments with both simulate and real data demonstrate that the proposed method is very efficient and robust.
基金This research is partially supported by NIH,No.R15EB024283.
文摘If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continuation theory suggests that a finite-sized object can be uniquely determined by its frequency components in a very small neighborhood.Trying to obtain such an exact Taylor expansion is difficult.This paper proposes an iterative algorithm to extend the measured frequency components to unmeasured regions.Computer simulations show that the proposed algorithm converges very slowly,indicating that the problem is too ill-posed to be practically solvable using available methods.
文摘In this paper, a new iterative solution method is proposed for solving multiple linear systems A(i)x(i)=b(i), for 1≤ i ≤ s, where the coefficient matrices A(i) and the right-hand sides b(i) are arbitrary in general. The proposed method is based on the global least squares (GL-LSQR) method. A linear operator is defined to connect all the linear systems together. To approximate all numerical solutions of the multiple linear systems simultaneously, the GL-LSQR method is applied for the operator and the approximate solutions are obtained recursively. The presented method is compared with the well-known LSQR method. Finally, numerical experiments on test matrices are presented to show the efficiency of the new method.
文摘In this paper, we introduce some new classes of the totally quasi-G-asymptotically nonexpansive mappings and the totally quasi-G-asymptotically nonexpansive semigroups. Then, with the generalized f-projection operator, we prove some strong convergence theorems of a new modified Halpern type hybrid iterative algorithm for the totally quasi-G-asymptotically nonexpansive semigroups in Banach space. The results presented in this paper extend and improve some corresponding ones by many others.
文摘针对一般超分辨率算法无法在重建效果和运行速度上取得较好的平衡,结合结构相似性提出了一种具有保边性的迭代反投影算法(iterative back projection,IBP)的超分辨率算法。兼顾算法运行速度,在传统的IBP基础上添加各项异性扩散,使之具有边缘增强和保边效果。为了结合更多的先验知识,将保边IBP和结构相似性结合在一起,使重建效果更加自然细腻。采用峰值信噪比和结构相似性度量评价算法效果。从实验结果数据可以看出,算法具有最高的PSNR值和SSIM值,其中SSIM的值最高可以达到0.95,非常接近于1。从实验结果图可以看出,算法的纹理保留的最好,图像更自然和准确。而且运行速度没有严重落后于传统IBP,具有很好的实用性。
基金Supported by the National Natural Science Foundation ofChina(No.61271240)Jiangsu Province Natural Science Fund Project(No.BK2010077)Subject of Twelfth Five Years Plans in Jiangsu Second Normal University(No.417103)
文摘Matrix completion is the extension of compressed sensing.In compressed sensing,we solve the underdetermined equations using sparsity prior of the unknown signals.However,in matrix completion,we solve the underdetermined equations based on sparsity prior in singular values set of the unknown matrix,which also calls low-rank prior of the unknown matrix.This paper firstly introduces basic concept of matrix completion,analyses the matrix suitably used in matrix completion,and shows that such matrix should satisfy two conditions:low rank and incoherence property.Then the paper provides three reconstruction algorithms commonly used in matrix completion:singular value thresholding algorithm,singular value projection,and atomic decomposition for minimum rank approximation,puts forward their shortcoming to know the rank of original matrix.The Projected Gradient Descent based on Soft Thresholding(STPGD),proposed in this paper predicts the rank of unknown matrix using soft thresholding,and iteratives based on projected gradient descent,thus it could estimate the rank of unknown matrix exactly with low computational complexity,this is verified by numerical experiments.We also analyze the convergence and computational complexity of the STPGD algorithm,point out this algorithm is guaranteed to converge,and analyse the number of iterations needed to reach reconstruction error.Compared the computational complexity of the STPGD algorithm to other algorithms,we draw the conclusion that the STPGD algorithm not only reduces the computational complexity,but also improves the precision of the reconstruction solution.
