Accelerated Randomized Coordinate Descent for Solving Linear Systems

Abstract

The randomized coordinate descent (RCD) method is a simple but powerful approach to solving inconsistent linear systems. In order to accelerate this approach, the Nesterov accelerated randomized coordinate descent method (NARCD) is proposed. The randomized coordinate descent with the momentum method (RCDm) is proposed by Nicolas Loizou, we will provide a new convergence boundary. The global convergence rates of the two methods are established in our paper. In addition, we show that the RCDm method has an accelerated convergence rate by choosing a proper momentum parameter. Finally, in numerical experiments, both the RCDm and the NARCD are faster than the RCD for uniformly distributed data. Moreover, the NARCD has a better acceleration effect than the RCDm and the Nesterov accelerated stochastic gradient descent method. When the linear correlation of matrix A is stronger, the NARCD acceleration is better.