论文标题
在放松的贪婪的确定性行和列迭代方法上
On the relaxed greedy deterministic row and column iterative methods
论文作者
论文摘要
For solving the large-scale linear system by iteration methods, we utilize the Petrov-Galerkin conditions and relaxed greedy index selection technique and provide two relaxed greedy deterministic row (RGDR) and column (RGDC) iterative methods, in which one special case of RGDR reduces to the fast deterministic block Kaczmarz method proposed in Chen and Huang (Numer. Algor., 89：1007-1029，2021）。我们的收敛分析表明，所得算法都具有线性收敛速率，这些算法受显式表达式的界定。数值示例表明，所提出的算法比松弛的贪婪随机行和柱迭代方法更有效。
For solving the large-scale linear system by iteration methods, we utilize the Petrov-Galerkin conditions and relaxed greedy index selection technique and provide two relaxed greedy deterministic row (RGDR) and column (RGDC) iterative methods, in which one special case of RGDR reduces to the fast deterministic block Kaczmarz method proposed in Chen and Huang (Numer. Algor., 89: 1007-1029, 2021). Our convergence analyses reveal that the resulting algorithms all have the linear convergence rates, which are bounded by the explicit expressions. Numerical examples show that the proposed algorithms are more effective than the relaxed greedy randomized row and column iterative methods.
