Chengyi Zhang

Lechao Cheng, Chengyi Zhang, Zicheng Liao

We introduce a new network structure for decomposing an image into its intrinsic albedo and shading. We treat this as an image-to-image transformation problem and explore the scale space of the input and output. By expanding the output images (albedo and shading) into their Laplacian pyramid components, we develop a multi-channel network structure that learns the image-to-image transformation function in successive frequency bands in parallel, within each channel is a fully convolutional neural network with skip connections. This network structure is general and extensible, and has demonstrated excellent performance on the intrinsic image decomposition problem. We evaluate the network on two benchmark datasets: the MPI-Sintel dataset and the MIT Intrinsic Images dataset. Both quantitative and qualitative results show our model delivers a clear progression over state-of-the-art.

Cheng-yi Zhang, Shuanghua Luo, Zongben Xu

The paper studies the convergence of some parallel multisplitting block iterative methods for the solution of linear systems arising in the numerical solution of Euler equations. Some sufficient conditions for convergence are proposed. As special cases the convergence of the parallel block generalized AOR (BGAOR), the parallel block AOR (BAOR), the parallel block generalized SOR (BGSOR), the parallel block SOR (BSOR), the extrapolated parallel BAOR and the extrapolated parallel BSOR methods are presented. Furthermore, the convergence of the parallel block iterative methods for linear systems with special block tridiagonal matrices arising in the numerical solution of Euler equations are discussed. Finally, some examples are given to demonstrate the convergence results obtained in this paper.

Cheng-yi Zhang, Dan Ye, Cong-lei Zhong et al.

It is well known that as a famous type of iterative methods in numerical linear algebra, Gauss-Seidel iterative methods are convergent for linear systems with strictly or irreducibly diagonally dominant matrices, invertible $H-$matrices (generalized strictly diagonally dominant matrices) and Hermitian positive definite matrices. But, the same is not necessarily true for linear systems with nonstrictly diagonally dominant matrices and general $H-$matrices. This paper firstly proposes some necessary and sufficient conditions for convergence on Gauss-Seidel iterative methods to establish several new theoretical results on linear systems with nonstrictly diagonally dominant matrices and general $H-$matrices. Then, the convergence results on preconditioned Gauss-Seidel (PGS) iterative methods for general $H-$matrices are presented. Finally, some numerical examples are given to demonstrate the results obtained in this paper.

Cheng-yi Zhang, Shuanghua Luo, Yan Zhu

To solve non-Hermitian linear system Ax=b on parallel and vector machines, some paralell multisplitting methods are considered. In this work, in particular: i) We establish the convergence results of the paralell multisplitting methods, together with its relaxed version, some of which can be regarded as generalizations of analogous results for the Hermitian positive definite case; ii) We extend the positive-definite and skew-Hermitian splitting (PSS) method methods in [{\em SIAM J. Sci. Comput.}, 26:844--863, 2005] to the parallel PSS methods and propose the corresponding convergence results.