求解大型线性方程组的带动量贪婪随机Kaczmarz方法

Greedy Randomized Kaczmarz Method with Momentum

基于一种新而有效的概率准则,白和巫构建了一个求解大型线性方程组的贪婪随机Kaczmarz(GRK)方法。结合贪婪策略和Heavy-Ball技术,提出了带动量GRK方法(mGRK),并且建立了mGRK方法的全局线性收敛性理论。最后,数值实验表明mGRK方法在迭代步数和计算时间方面均优于GRK方法。

Based on a new and effective probability criterion,Bai and Wu constructed a greedy randomized Kaczmarz(GRK)method for solving large linear systems.In this paper,a momentum variant of GRK(mGRK)method is developed by combining greedy technique and Heavy-Ball technique.The global linear convergence rate of the new method is established.Finally,numerical results show that the proposed mGRK method converges faster than the GRK method in terms of iteration steps and computing times.