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In this paper, we introduce a preconditioned Euler-extrapolated single-step Hermitian and skew-Hermitian splitting (PE-SHSS) iteration method for solving a class of complex symmetric system of linear equations. The convergence properties of the PE-SHSS iteration method are investigated under suitable restrictions. In addition, the spectral properties of the corresponding preconditioned matrix are discussed. Finally, three numerical examples are also used to verify the effectiveness of the PE-SHSS iteration method.

In this paper, we first present some simple approaches to obtain dual and approximate dual g-frames. Then, we show that approximate dual g-frames are stable under some conditions. Finally, we give ...

In this paper, a lopsided modified Euler-extrapolated Hermitian and skew-Hermitian splitting (LME-HS) iteration method is introduced for solving the complex symmetric linear systems. Under a loose restriction on parameter $\theta$, we demonstrate that LME-HS iteration method is convergent. Moreover, we present the optimal parameter ${\theta}^{*}$ of the LME-HS method and discuss the spectral properties of corresponding preconditioned matrix. Finally, the numerical experiments are used to verify the effectiveness of the proposed method.

The problem of serious air pollution such as haze and fog and other complex scenes has posed great challenges for target tracking in computer vision. Single-feature approaches demonstrating unstable performances lead to poor tracking. Through the multi-feature fusion and the focus of attention (FOA) mechanism in biological vision system, these problems under complex scenes can be solved. Accordingly, a tracking algorithm based on multi-feature fusion and spatio-context correlation is proposed. Accurate expression of multi-feature fusion by color, texture, and edge features, and adaptive weighted update by information entropy, has greatly enhanced the adaptability to environment variations. Then, combined with the spatio-temporal context algorithm, the target can be achieved accurately. Compared with the state-of-the-art tracking algorithms, the experiment results validate the effectiveness of our method in hazy scenes, furthermore, our method also results in the promotion of image vision quality. Specifically, the average center error is reduced to 0.9440 pixel, and the average overlap rate and the FPS rise to 0.8700 and 4.4302, respectively. Additionally, the halo artifacts and color cast of restored images have been avoided by the popular dehazing algorithm. Our proposed tracking algorithm outperforms the state-of-the-art methods in accuracy, robustness, and real-time even in complex real-world hazy scenes.

Transmission estimation is the most challenging part for single image haze removal and very sensitive to environment noise. However, most existing single image dehazing algorithms are far from satisfactory in terms of restoring an image’s details and noise removal. To address this issue, an improved haze imaging model with transmission refinement based on dark channel prior is constructed to preserve the edge details and enhance visibility. Then, a fast single image dehazing algorithm called TSGA algorithm is proposed for complex real-world images. A refined transmission map obtained by TGVSH regularity scheme provides more edges and finer details and is less susceptible to noise. Guided filter and adaptive histogram equalization greatly enhance the visibility and color contrast of the scenes and significantly improve the drawback of halo artifacts. A large quantity of comparative experiment results demonstrate that the proposed algorithm simultaneously removes the serious effect of haze and noise, effectively makes the restored images look more natural, and has a lower time complexity. All these make it a good candidate for image segmentation, object recognition, and target tracking in complex real-world weather conditions.

Recently, two families of HSS-based iteration methods are constructed for solving the system of absolute value equations (AVEs), which is a class of non-differentiable NP-hard problems. In this study, we establish the Picard-CSCS iteration method and the nonlinear CSCS-like iteration method for AVEs involving the Toeplitz matrix. Then, we analyze the convergence of the Picard-CSCS iteration method for solving AVEs. By using the theory about nonsmooth analysis, we particularly prove the convergence of the nonlinear CSCS-like iterationsolver for AVEs. The advantage of these methods is that they do not require the storage of coefficient matrices at all, and the sub-system of linear equations can be solved efficiently via the fast Fourier transforms (FFTs). Therefore, computational cost and storage can be saved in practical implementations. Numerical examples including numerical solutions of nonlinear fractional diffusion equations are reported to show the effectiveness of the proposed methods in comparison with some existing methods., Comment: 22 pages, 2 figures. This manuscript has been accepted (by J. Appl. Anal. Comput., in press) for publication (2017/02). arXiv admin note: text overlap with arXiv:1403.7013 by other authors

In this paper, using the quadratic spline collocation method (QSC), we numerically solve the Helmholtz equations with the Sommerfeld boundary conditions. By reordering the unknowns, we obtain a $$3\times 3$$ block linear system. Then, we introduce a two-step preconditioner based on the approximate inverse block polynomial preconditioner. Theoretical analysis show this preconditioner can largely gather the eigenvalues around 1. Numerical examples are presented to test the error of QSC method and check the efficiency of the presented preconditioner.

As is well-known, the advantage of the high-order compact difference scheme (H-OCD) is that it is unconditionally stable and convergent on the order O ( &tau, 2 + h 4 ) (where &tau, is the time step size and h is the mesh size), under the maximum norm for a class of nonlinear delay partial differential equations with initial and Dirichlet boundary conditions. In this article, a new numerical gradient scheme based on the collocation polynomial and Hermite interpolation is presented. The convergence order of this kind of method is also O ( &tau, 2 + h 4 ) under the discrete maximum norm when the spatial step size is twice the one of H-OCD, which accelerates the computational process. In addition, some corresponding analyses are made and the Richardson extrapolation technique is also considered in the time direction. The results of numerical experiments are consistent with the theoretical analysis.