Dr. Lu Wang, School of Mathematical Sciences, Hebei Normal University

Zhongzhi Bai, Professor

On Convergence Analysis of the Randomized Kaczmarz Method and the Randomized Gauss-Seidel Method

21:00-22:00 October 26 (Wednesday), Tencent Meeting ID: 563-304-160

The randomized Kaczmarz method and the randomized Gauss-Seidel method are two classical randomized iteration methods for solving systems of linear equations, which operate in column and row spaces, respectively. In this report, we firstly introduce some convergence results of the randomized Kaczmarz method and its variants. Then by utilizing the inner connections between the randomized Kaczmarz method and the randomized Gauss-Seidel method, we give a new upper bound for the convergence rate of the randomized Gauss-Seidel method. Moreover, these convergence results are also extended to the more general extrapolated randomized Gauss-Seidel method.