求解相干线性方程组的稀疏惯性随机Kaczmarz算法

SPARSE INERTIAL RANDOMIZED KACZMARZ ALGORITHMS FOR COHERENT LINEAR SYSTEMS

双子空间投影算法和多步惯性随机Kaczmarz算法是求解相干线性方程组的有效算法,本文通过软阈值函数对这两种算法进行修正,提出了稀疏双子空间投影算法和稀疏多步惯性随机Kaczmarz算法,并给出其在有噪声干扰和无噪声干扰情况下在期望意义下的线性收敛率估计.通过数值实验验证本文所提算法的有效性和优越性.

The two-subspace projection algorithm and the multi-step inertial randomized Kaczmarz algorithm are effective methods for solving the coherent linear system.By adding the soft shrinkage in the two-subspace projection algorithm and the multi-step inertial randomized Kaczmarz algorithm,this paper introduces the sparse two-subspace projection algorithm and the sparse multi-step inertial randomized Kaczmarz algorithm.The linear convergence rate in expectation of the proposed algorithms in noise and noiseless cases is presented.Finally,we give some numerical experiments to illustrate the effectiveness and advantage of our algorithms.