In this paper,we consider the so-called "inexact Uzawa" algorithm applied to the unstable Navier-Stokes problem.We use stabilization matrix to stabilize the unstable system and proved theoretically that unde...In this paper,we consider the so-called "inexact Uzawa" algorithm applied to the unstable Navier-Stokes problem.We use stabilization matrix to stabilize the unstable system and proved theoretically that under given proper preconditioners,Uzawa algorithm is convergent for the stablization system.Bounds for the iteration error are provided.We show numerically that Uzawa algorithm is convergent as well for the stabilization systems when it is used in the steady-state Navier-Stokes problem(cf.[6]).展开更多
Density-based clustering is an important category among clustering algorithms. In real applications, many datasets suffer from incompleteness. Traditional imputation technologies or other techniques for handling missi...Density-based clustering is an important category among clustering algorithms. In real applications, many datasets suffer from incompleteness. Traditional imputation technologies or other techniques for handling missing values are not suitable for density-based clustering and decrease clustering result quality. To avoid these problems,we develop a novel density-based clustering approach for incomplete data based on Bayesian theory, which conducts imputation and clustering concurrently and makes use of intermediate clustering results. To avoid the impact of low-density areas inside non-convex clusters, we introduce a local imputation clustering algorithm, which aims to impute points to high-density local areas. The performances of the proposed algorithms are evaluated using ten synthetic datasets and five real-world datasets with induced missing values. The experimental results show the effectiveness of the proposed algorithms.展开更多
文摘In this paper,we consider the so-called "inexact Uzawa" algorithm applied to the unstable Navier-Stokes problem.We use stabilization matrix to stabilize the unstable system and proved theoretically that under given proper preconditioners,Uzawa algorithm is convergent for the stablization system.Bounds for the iteration error are provided.We show numerically that Uzawa algorithm is convergent as well for the stabilization systems when it is used in the steady-state Navier-Stokes problem(cf.[6]).
基金supported by the National Natural Science Foundation of China(Nos.U1866602 and 71773025)the National Key Research and Development Program of China(No.2020YFB1006104)
文摘Density-based clustering is an important category among clustering algorithms. In real applications, many datasets suffer from incompleteness. Traditional imputation technologies or other techniques for handling missing values are not suitable for density-based clustering and decrease clustering result quality. To avoid these problems,we develop a novel density-based clustering approach for incomplete data based on Bayesian theory, which conducts imputation and clustering concurrently and makes use of intermediate clustering results. To avoid the impact of low-density areas inside non-convex clusters, we introduce a local imputation clustering algorithm, which aims to impute points to high-density local areas. The performances of the proposed algorithms are evaluated using ten synthetic datasets and five real-world datasets with induced missing values. The experimental results show the effectiveness of the proposed algorithms.
