The linearized Bregman iterative (LBI) algorithm is an efficient method of dealing with the famous basis pursuit problem. In this paper, we study the convergence of the fast linearized Bregman iterative (F-LBI) algorithm. First of all, on the basis of the theory analysis of F-LBI by Osher et al, we conclude that the sequence by the F-LBI is not definite of the subsequence of the LBI. Then we take the error into account and derive a strict convergence result by comparison analysis between the LBI and F-LBI.
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