求解大型稀疏线性系统的贪婪双子空间随机Kaczmarz方法

A Greedy Two-Subspace Randomized Kaczmarz Method for Solving Large Sparse Linear Systems

摘要:

基于一种有效的从系数矩阵中选取两个工作行的贪婪概率准则， 提出一类求解大型稀疏线性系统的贪婪双子空间随机Kaczmarz方法。理论证明该方法收敛到相容线性系统的最小范数解， 而且该方法的理论收敛因子小于原始双子空间随机Kaczmarz方法的收敛因子。数值实验表明，该方法在求解性能方面较原始双子空间随机Kaczmarz方法更具优势。

Abstract:

Based on an effective greedy probability criterion for selecting two working rows from a coefficient matrix， a greedy two-subspace randomized Kaczmarz method for solving large sparse linear systems is proposed. The theoretical analysis shows that this method converges to the minimal-norm solution of consistent linear systems， and the convergence factor of the method is smaller than that of the original two-subspace randomized Kaczmarz method. The numerical experiments show that this method is superior to the original two-subspace randomized Kaczmarz method from the point of view of solution performance.