The randomized block Kaczmarz(RBK)method is a randomized orthogonal projection iterative approach,which plays an important role in solving large-scale linear systems.A key point of this type of method is to select wor...The randomized block Kaczmarz(RBK)method is a randomized orthogonal projection iterative approach,which plays an important role in solving large-scale linear systems.A key point of this type of method is to select working rows effectively during iterations.However,in most of the RBK-type methods,one has to scan all the rows of the coefficient matrix in advance to compute probabilities or paving,or to compute the residual vector of the linear system in each iteration to determine the working rows.These are unfavorable for big data problems.To cure these drawbacks,we propose a semi-randomized block Kaczmarz(SRBK)method with simple random sampling for large-scale linear systems in this paper.The convergence of the proposed method is established.Numerical experiments on some real-world and large-scale data sets show that the proposed method is often superior to many state-of-the-art RBK-type methods for large linear systems.展开更多
One of the most important issues in inertial confinement fusion (ICF) is to study the uniformity of the radiation field around the implosion pellet containing fuel.To this end,a numerical method linking Monte Carlo wi...One of the most important issues in inertial confinement fusion (ICF) is to study the uniformity of the radiation field around the implosion pellet containing fuel.To this end,a numerical method linking Monte Carlo with iteration method is presented for calculating the radiation transfer problems in a cavity.The detail of the calculation scheme is described and some numerical examples are also given.展开更多
基金National Natural Science Foundation of China under grant 12271518the Fujian Natural Science Foundation under grant 2023J01354+1 种基金the Key Research and Development Project of Xuzhou Natural Science Foundation under grant KC22288the Open Project of Key Laboratory of Data Science and Intelligence Education of the Ministry of Education under grant DSIE202203。
文摘The randomized block Kaczmarz(RBK)method is a randomized orthogonal projection iterative approach,which plays an important role in solving large-scale linear systems.A key point of this type of method is to select working rows effectively during iterations.However,in most of the RBK-type methods,one has to scan all the rows of the coefficient matrix in advance to compute probabilities or paving,or to compute the residual vector of the linear system in each iteration to determine the working rows.These are unfavorable for big data problems.To cure these drawbacks,we propose a semi-randomized block Kaczmarz(SRBK)method with simple random sampling for large-scale linear systems in this paper.The convergence of the proposed method is established.Numerical experiments on some real-world and large-scale data sets show that the proposed method is often superior to many state-of-the-art RBK-type methods for large linear systems.
基金Project supported in part by the National Natural Science Foundation of China and the National High-Tech ICF Committee in China.
文摘One of the most important issues in inertial confinement fusion (ICF) is to study the uniformity of the radiation field around the implosion pellet containing fuel.To this end,a numerical method linking Monte Carlo with iteration method is presented for calculating the radiation transfer problems in a cavity.The detail of the calculation scheme is described and some numerical examples are also given.
文摘孤立森林是一种高效的异常检测算法,但其轴平行线隔离的方式难以检测到非线性可分离数据中的异常。针对此问题,提出了一种利用神经网络随机投影融合孤立森林(isolation Forest, iForest)的半监督离群点检测方法——稀疏深度随机映射正向隔离林(Sparse deep Random Projection Positive isolation Forest, SRP-PiF)。算法通过神经网络进行非线性随机映射,将不同大小的子空间进行非线性划分,为分类提供有效的低维特征属性;设置超参数稀疏率来调整神经元中的权重,提高运算效率,最后结合半监督学习方式进行训练和预测。所提方法在真实世界10个数据集上进行验证,结果表明:相比于同类异常检测算法,SRP-PiF在异常检测性能指标AUC-ROC中有明显提升;在样本数量较多的数据集下,该算法识别精确度比孤立森林算法和经验累积分布函数的无监督离群值检测方法(ECOD)高出3%~20%。
