A greedy average block sparse Kaczmarz method is developed for the sparse solution of the linear system of equations. The convergence theory of this method is established and the upper bound of its convergence rate with adaptive stepsize is derived. Numerical experiments are presented to verify the efficiency of the proposed method, which outperforms the existing sparse Kaczmarz methods in terms of the number of iteration steps and computational costs.

中文翻译：

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线性系统稀疏解的贪心平均块稀疏Kaczmarz方法

针对线性方程组的稀疏解，提出了一种贪婪平均块稀疏Kaczmarz方法。建立了该方法的收敛理论，并推导了自适应步长下该方法的收敛速度上界。数值实验验证了该方法的效率，该方法在迭代步数和计算成本方面优于现有的稀疏 Kaczmarz 方法。