期刊
LINEAR ALGEBRA AND ITS APPLICATIONS
卷 652, 期 -, 页码 132-154出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.laa.2022.07.003
关键词
Randomized Kaczmarz method; Sparse solutions; Least squares; Impulsive noise
资金
- ITN-ETN project TraDE-OPT - European Union's Horizon 2020 research and innovation programme [861137]
- Marie Curie Actions (MSCA) [861137] Funding Source: Marie Curie Actions (MSCA)
This article introduces the combination of the Extended Randomized Kaczmarz method and the Sparse Randomized Kaczmarz method, proposing the Extended Sparse Randomized Kaczmarz method. The effectiveness of the method in handling noise problems is verified through numerical experiments.
The Extended Randomized Kaczmarz method is a well known iterative scheme which can find the Moore-Penrose inverse solution of a possibly inconsistent linear system and requires only one additional column of the system matrix in each iteration in comparison with the standard randomized Kaczmarz method. Also, the Sparse Randomized Kaczmarz method has been shown to converge linearly to a sparse solution of a consistent linear system. Here, we combine both ideas and propose an Extended Sparse Randomized Kaczmarz method. We show linear expected convergence to a sparse least squares solution in the sense that an extended variant of the regularized basis pursuit problem is solved. Moreover, we generalize the additional step in the method and prove convergence to a more abstract optimization problem. We demonstrate numerically that our method can find sparse least squares solutions of real and complex systems if the noise is concentrated in the complement of the range of the system matrix and that our generalization can handle impulsive noise.(c) 2022 Elsevier Inc. All rights reserved.
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