%0 Journal Article
%T 新的加速Bregman迭代方法在稀疏最小二乘问题中的应用<br>Application of a new accelerating Bregman iterative algorithm in the sparse least squares problems
%A 王文淑
%A 李维国
%A 秦淑兰&lt
%A br&gt
%A WANG Wen-shu
%A LI Wei-guo
%A QIN Shu-lan
%J 山东大学学报（理学版）
%D 2016
%R 10.6040/j.issn.1671-9352.4.2015.004
%X 摘要： 结合残量Bregman迭代方法以及不动点迭代方法提出一种迭代算法,对预测校正算法应用Nesterov技巧进行加速,并且作用于最小二乘问题。理论上证明了新算法得到的解收敛到目标函数的最优解,并将新算法应用到稀疏信号恢复问题上,数值试验表明新算法能够快速有效地恢复信号。<br>Abstract: Based on the residual Bregman iterative algorithm and fixed point iteration, a novel Bregman iterative algorithm is proposed. Then, inspired by the equivalence of the linearized Bregman and the gradient descent algorithm of the dual problem, a new algorithm by introducing Nesterov accelerating technique into the predictor-corrector method is put forward for solving the sparse least squares problems. Simultaneously, It is proved that the solution sequence obtained by the new method is the optimal solution of the sparse least squares problems. Finally, we use the new method to the sparse signal recovery problem. The numerical results show that the new method is faster and more efficientthan the old ones
%K 稀疏最小二乘问题
%K Nesterov加速技巧
%K Bregman迭代
%K &lt
%K br&gt
%K Nesterov accelerating technique
%K Bregman iteration
%K the sparse least squares problems
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.4.2015.004