Sparse Sampling Kaczmarz-Motzkin Method with Linear Convergence

Mathematical Methods In The Applied Sciences（2021）SCI 4区

Acad Mil Sci Peoples Liberat Army

Cited 7|Views42

Abstract

The randomized sparse Kaczmarz method was recently proposed to recover sparse solutions of linear systems. In this work, we introduce a greedy variant of the randomized sparse Kaczmarz method by employing the sampling Kaczmarz-Motzkin method and prove its linear convergence in expectation with respect to the Bregman distance in the noiseless and noisy cases. This greedy variant can be viewed as a unification of the sampling Kaczmarz-Motzkin method and the randomized sparse Kaczmarz method, and hence inherits the merits of these two methods. Numerically, we report a couple of experimental results to demonstrate its superiority.

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Key words

Bregman projection,sampling Kaczmarz-Motzkin,sparse

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