Abstract
In order to solve large scale consistent linear systems, based on the Kaczmarz algorithm, we propose two Multi-step Randomized Kaczmarz algorithms, denoted as MRK1 and MRK2, and give the corresponding convergence analysis. We consider using parameters to control the number of working rows. MRK1 algorithm uses a fixed parameter <i>m</i>, and the best result is that the parameter <i>m</i> is the number of rows of the coefficient matrix, while MRK2 algorithm uses a randomly generated parameter <i>m</i>, which is more general. Finally, we carry out the corresponding numerical simulation experiments, the experimental results show that, compared with the RK, GRK algorithm, the new algorithm is faster and more efficient on CPU in most cases, and the maximum CPU acceleration is 12.54. And the difference between MRK1(s), MRK2 and MGRK on CPU is not very significant according to experimental results.
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