论文标题
无假的随机块迭代算法，以使一致且不一致的线性系统不一致
Pseudoinverse-free randomized block iterative algorithms for consistent and inconsistent linear systems
论文作者
论文摘要
近年来，随机迭代算法引起了很多关注，因为它们可以大致求解大规模线性方程式，而无需访问整个系数矩阵。在本文中，我们提出了两种新型的无伪随机块迭代算法，以求解一致且不一致的线性系统。所提出的算法需要两个用户定义的随机矩阵：一个用于行采样，另一个用于列采样。我们可以通过选择我们算法中使用的适当随机矩阵，恢复众所周知的双重随机高斯 - seidel，seidel，随机kaczmarz，随机坐标下降和随机扩展的kaczmarz算法。因为我们的算法允许对这两个随机矩阵进行更广泛的选择，因此可以获得许多新的特定算法。我们证明了我们算法的均等意义中的线性收敛。具有合成和现实系数矩阵的线性系统的数值实验证明了我们算法的某些特殊情况的效率。
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel pseudoinverse-free randomized block iterative algorithms for solving consistent and inconsistent linear systems. The proposed algorithms require two user-defined random matrices: one for row sampling and the other for column sampling. We can recover the well-known doubly stochastic Gauss--Seidel, randomized Kaczmarz, randomized coordinate descent, and randomized extended Kaczmarz algorithms by choosing appropriate random matrices used in our algorithms. Because our algorithms allow for a much wider selection of these two random matrices, a number of new specific algorithms can be obtained. We prove the linear convergence in the mean square sense of our algorithms. Numerical experiments for linear systems with synthetic and real-world coefficient matrices demonstrate the efficiency of some special cases of our algorithms.
