基于残差驱动的块Kaczmarz算法研究

RESEARCH ON KACZMARZ ALGORITHM BASED ON RESIDUALDRIVE

针对大型稀疏线性方程组求解问题,本文以块Kaczmarz方法的思想为基础,提出了一种新的随机块Kaczmarz算法一随机贪婪残差块Kaczmarz(GREBK(k))算法.首先,利用K-means聚类算法对标准化残差进行聚类分块,获得系数矩阵中对应的行分块策略;针对上述分块方式,再进行随机贪婪块Kaczmarz方法求解。相关理论分析证明了该算法的收敛性,最后,数值实验表明GREBK(k)算法改进了目前现有相关结果,是一种行之有效的数值方法.

For solving large sparse linear equations,based on the idea of block Kaczmarz method,this paper proposes a new random block Kaczmarz algorithmrandom greedy residual block Kaczmarz(GREBK(k))algorithm.Firstly,the K-means clustering algorithm is used to partition the standardized residuals and obtain the corresponding row partitioning strategy in the coeficient matrix,and then solves these equations by the random greedy block Kaczmarz for the above blocked mode.The convergence of this algorithm is proved by relevant theoretical analysis.Finally,numerical experiments show that GREBK(k)algorithm greatly improves the existing relevant results and is an effective numerical method.