贪婪随机扩展Kaczmarz算法研究
Research on Greedy Random Extended Kaczmarz Algorithm
摘要: 求解大规模线性方程组的问题广泛存在于各个研究领域。求解这一问题的方法有很多，其中，Kaczmarz迭代算法的研究更为广泛，该算法用于超定、欠定系统。本文分析了国内外关于Kaczmarz扩展算法与贪婪算法相结合的分块算法，并提出贪婪随机双块Kaczmarz算法(GRDBK)。GRDBK在REK算法和GRK算法的基础上进行创新，适用于超定不相容的线性系统。
Abstract: The problem of solving large-scale linear systems of equations widely exists in various research fields. There are many methods to solve this problem, among which Kaczmarz iterative algorithm is more widely studied, and it is used for overdetermined and underdetermined systems. In this paper, we analyze the algorithm combining Kaczmarz extension algorithm with greedy algorithm at home and abroad, and propose greedy random double block Kaczmarz algorithm (GRDBK). GRDBK innovates on the basis of REK algorithm and GRK algorithm, and is suitable for overdetermined and inconsistent linear system.
文章引用：张卜月. 贪婪随机扩展Kaczmarz算法研究[J]. 理论数学, 2023, 13(1): 113-119. https://doi.org/10.12677/PM.2023.131013

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