Recently, Elfving, Hansen, and Nikazad introduced a successful nonstationary block‐column iterative method for solving linear system of equations based on flagging idea (called BCI‐F). Their numerical tests show that the column‐action method provides a basis for saving computational work using flagging technique in BCI algorithm. However, they did not present a general convergence analysis. In this paper, we give a convergence analysis of BCI‐F. Furthermore, we consider a fully flexible version of block‐column iterative method (FBCI), in which the relaxation parameters and weight matrices can be updated in each iteration and the column partitioning of coefficient matrix is allowed to update in each cycle. We also provide the convergence analysis of algorithm FBCI under mild conditions.

中文翻译：

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关于非平稳列式代数迭代方法的收敛性

最近，Elfving，Hansen和Nikazad提出了一种成功的非平稳块列迭代方法，该方法基于标记思想（称为BCI-F）来求解线性方程组。他们的数值测试表明，列作用方法为使用BCI算法中的标记技术节省计算工作量提供了基础。但是，他们没有提出一般的收敛分析。在本文中，我们给出了BCI-F的收敛性分析。此外，我们考虑了完全灵活的块列迭代方法（FBCI）版本，其中可以在每次迭代中更新松弛参数和权重矩阵，并允许在每个周期中更新系数矩阵的列划分。我们还提供了在温和条件下算法FBCI的收敛性分析。