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DOI: 10.23952/jnfa.2022.2
Received June 2, 2021; Accepted November 25, 2021; Published February 23, 2022
Abstract In this paper, we first introduce a modified randomized Kaczmarz algorithm, and obtain a better convergence rate estimate than that of the randomized Kaczmarz algorithm. Second, we study a greedy Kaczmarz algorithm, which can be regarded as a simplification of the greedy randomized Kaczmarz algorithm. A deterministic (not in the sense of expectation) convergence rate estimate is obtained for the greedy Kaczmarz algorithm. We find that the greedy Kaczmarz algorithm not only needs less computational workload in each iteration, but also has faster convergence speed than the greedy randomized Kaczmarz algorithm. Numerical results are provided to support the theoretical analysis in this paper.
How to Cite this Article:
S. He, Z. Wang, X. Qin, Some improvements of randomized Kaczmarz algorithms, J. Nonlinear Funct. Anal. 2022 (2022) 2.