In this paper,we propose hierarchical absorbing interface conditions to solve the problem of wave propagation in domains with a non-uniform space discretization or grid size inhomogeneity using Pad´e Via Lanczos(...In this paper,we propose hierarchical absorbing interface conditions to solve the problem of wave propagation in domains with a non-uniform space discretization or grid size inhomogeneity using Pad´e Via Lanczos(PVL)method.The proposed interface conditions add an auxiliary variable in the wave system to eliminate the spurious reflection at the interface between regions with different mesh sizes.The auxiliary variable with proper boundary condition can suppress the spurious reflection by cancelling the boundary source term produced by the space inhomogeneity in variational perspective.The new hierarchical interface conditions with the help of PVL implementation can effectively reduce the degree of freedom in solving the wave propagation problem.展开更多
Truncated L1 regularization proposed by Fan in[5],is an approximation to the L0 regularization in high-dimensional sparse models.In this work,we prove the non-asymptotic error bound for the global optimal solution to ...Truncated L1 regularization proposed by Fan in[5],is an approximation to the L0 regularization in high-dimensional sparse models.In this work,we prove the non-asymptotic error bound for the global optimal solution to the truncated L1 regularized linear regression problem and study the support recovery property.Moreover,a primal dual active set algorithm(PDAS)for variable estimation and selection is proposed.Coupled with continuation by a warm-start strategy leads to a primal dual active set with continuation algorithm(PDASC).Data-driven parameter selection rules such as cross validation,BIC or voting method can be applied to select a proper regularization parameter.The application of the proposed method is demonstrated by applying it to simulation data and a breast cancer gene expression data set(bcTCGA).展开更多
基金supported by the National Key Research and Development Program of China(Grant No.2020YFA0714200)by the National Natural Science Foundation of China(Grants No.12125103,12071362,12101062)+1 种基金by China Postdoctoral Sci-ence Foundation(Grant No.2019M660558)by the Natural Science Foundation of Hubei Province(Grant No.2019CFA007)。
文摘In this paper,we propose hierarchical absorbing interface conditions to solve the problem of wave propagation in domains with a non-uniform space discretization or grid size inhomogeneity using Pad´e Via Lanczos(PVL)method.The proposed interface conditions add an auxiliary variable in the wave system to eliminate the spurious reflection at the interface between regions with different mesh sizes.The auxiliary variable with proper boundary condition can suppress the spurious reflection by cancelling the boundary source term produced by the space inhomogeneity in variational perspective.The new hierarchical interface conditions with the help of PVL implementation can effectively reduce the degree of freedom in solving the wave propagation problem.
文摘Truncated L1 regularization proposed by Fan in[5],is an approximation to the L0 regularization in high-dimensional sparse models.In this work,we prove the non-asymptotic error bound for the global optimal solution to the truncated L1 regularized linear regression problem and study the support recovery property.Moreover,a primal dual active set algorithm(PDAS)for variable estimation and selection is proposed.Coupled with continuation by a warm-start strategy leads to a primal dual active set with continuation algorithm(PDASC).Data-driven parameter selection rules such as cross validation,BIC or voting method can be applied to select a proper regularization parameter.The application of the proposed method is demonstrated by applying it to simulation data and a breast cancer gene expression data set(bcTCGA).
