On greedy randomized average block Kaczmarz method for solving large linear systems
On greedy randomized average block Kaczmarz method for solving large linear systems
复制标题
求解大型线性系统的贪婪随机平均分块Kaczmarz方法
DOI：
10.1016/j.cam.2022.114372
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发表时间：
2022
影响因子：
2.4
通讯作者：
Wen-Ting Wu
中科院分区：
文献类型：
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作者：
Cun-Qiang Miao;Wen-Ting Wu
受贪婪随机化Kaczmarz方法的启发，我们提出了一个概率准则，该准则可以捕获残差的范数相对较大的子向量。根据这个概率准则，我们从系数矩阵中随机选取一个子矩阵，然后将当前迭代向量在这个子矩阵的每一行上的投影取平均，构造了求解相容线性方程组的贪婪随机平均块Kaczmarz方法，该方法可以在分布式环境中实现.当每个块的大小为1时，贪婪随机平均块Kaczmarz方法中的概率准则是贪婪随机Kaczmarz方法中的概率准则的推广。贪婪随机Kaczmarz方法也是贪婪随机平均块Kaczmarz方法的一个特例。分析了贪婪随机平均块Kaczmarz方法的两种外推步长。实验结果表明，贪婪随机平均块Kaczmarz方法的优点比贪婪随机Kaczmarz方法和现有的几个随机块Kaczmarz方法。
Inspired by the greedy randomized Kaczmarz method, we propose a probability criterion which can capture subvectors of the residual whose norms are relatively large. According to this probability criterion we select a submatrix randomly from the coefficient matrix, then average the projections of the current iteration vector onto each individual row of this chosen submatrix, constructing the greedy randomized average block Kaczmarz method for solving the consistent system of linear equations, which can be implemented in a distributed environment. When the size of each block is one, the probability criterion in the greedy randomized average block Kaczmarz method is a generalization of that in the greedy randomized Kaczmarz method. The greedy randomized Kaczmarz method is also a special case of the greedy randomized average block Kaczmarz method. Two kinds of extrapolated stepsizes for the greedy randomized average block Kaczmarz method are analyzed. The experimental results show the advantage of the greedy randomized average block Kaczmarz method over the greedy randomized Kaczmarz method and several existing randomized block Kaczmarz methods.