Richardson迭代法是求解ℳ张量多线性系统的一种有效方法。为了进一步加快其收敛速度,本文给出一个新的预处理子并提出一种新预处理Richardson迭代法。理论上证明所提预处理Richardson迭代法的收敛性。最后,通过数值例子验证该方法的有...Richardson迭代法是求解ℳ张量多线性系统的一种有效方法。为了进一步加快其收敛速度,本文给出一个新的预处理子并提出一种新预处理Richardson迭代法。理论上证明所提预处理Richardson迭代法的收敛性。最后,通过数值例子验证该方法的有效性和可行性。The Richardson iterative method is an effective method for solving multi-linear systems with ℳ-tensors. In this paper, a new preconditioner and new preconditioned Richardson iterative method are proposed to accelerate the convergence of multi-linear systems with ℳ-tensors. In the theory, the convergence of the preconditioned Richardson iterative method is proved. Finally, a numerical example is given to verify the effectiveness and feasibility of the proposed method.展开更多
求解大型线性系统,带K-均值聚类的贪婪随机块Kaczmarz方法是近几年被广受关注的一类方法。本文在该方法基础上做了进一步的研究即在每一次迭代中优先消除残差向量中的最大块,构建了最大残差块Kaczmarz方法及其加速版本并进行了收敛性分...求解大型线性系统,带K-均值聚类的贪婪随机块Kaczmarz方法是近几年被广受关注的一类方法。本文在该方法基础上做了进一步的研究即在每一次迭代中优先消除残差向量中的最大块,构建了最大残差块Kaczmarz方法及其加速版本并进行了收敛性分析。数值实验证实了本文算法的有效性。The greedy random block Kaczmarz method with K-means clustering for solving large linear systems has been widely studied in recent years. This article conducted further research on this method by prioritizing the elimination of the largest block in the residual vector in each iteration, constructing the Kaczmarz method for the maximum residual block and its accelerated version, and conducting convergence analysis. Numerical experiments have confirmed the effectiveness of the algorithm proposed in this paper.展开更多
文摘Richardson迭代法是求解ℳ张量多线性系统的一种有效方法。为了进一步加快其收敛速度,本文给出一个新的预处理子并提出一种新预处理Richardson迭代法。理论上证明所提预处理Richardson迭代法的收敛性。最后,通过数值例子验证该方法的有效性和可行性。The Richardson iterative method is an effective method for solving multi-linear systems with ℳ-tensors. In this paper, a new preconditioner and new preconditioned Richardson iterative method are proposed to accelerate the convergence of multi-linear systems with ℳ-tensors. In the theory, the convergence of the preconditioned Richardson iterative method is proved. Finally, a numerical example is given to verify the effectiveness and feasibility of the proposed method.
文摘求解大型线性系统,带K-均值聚类的贪婪随机块Kaczmarz方法是近几年被广受关注的一类方法。本文在该方法基础上做了进一步的研究即在每一次迭代中优先消除残差向量中的最大块,构建了最大残差块Kaczmarz方法及其加速版本并进行了收敛性分析。数值实验证实了本文算法的有效性。The greedy random block Kaczmarz method with K-means clustering for solving large linear systems has been widely studied in recent years. This article conducted further research on this method by prioritizing the elimination of the largest block in the residual vector in each iteration, constructing the Kaczmarz method for the maximum residual block and its accelerated version, and conducting convergence analysis. Numerical experiments have confirmed the effectiveness of the algorithm proposed in this paper.
