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With a quite different way to determine the working rows, we propose a novelgreedy Kaczmarz method for solving consistent linear systems. Convergenceanalysis of the new method is provided. Numerical experiments show that, forthe same accuracy, our method outperforms the greedy randomized Kaczmarz methodand the relaxed greedy randomized Kaczmarz method introduced recently by Baiand Wu [Z.Z. BAI AND W.T. WU, On greedy randomized Kaczmarz method for solvinglarge sparse linear systems, SIAM J. Sci. Comput., 40 (2018), pp. A592--A606;Z.Z. BAI AND W.T. WU, On relaxed greedy randomized Kaczmarz methods for solvinglarge sparse linear systems, Appl. Math. Lett., 83 (2018), pp. 21--26] in termof the computing time.

A Novel Greedy Kaczmarz Method For Solving Consistent Linear Systems