A randomized block Douglas–Rachford method for solving linear matrix equation

Abstract

The Douglas-Rachford method (DR) is one of the most computationally efficient iterative methods for the large scale linear systems of equations. Based on the randomized alternating reflection and relaxation strategy, we propose a randomized block Douglas–Rachford method for solving the matrix equation \(AXB=C\). The Polyak’s and Nesterov-type momentums are integrated into the randomized block Douglas–Rachford method to improve the convergence behaviour. The linear convergence of the resulting algorithms are proven. Numerical simulations and experiments of randomly generated data, real-world sparse data, image restoration problem and tensor product surface fitting in computer-aided geometry design are performed to illustrate the feasibility and efficiency of the proposed methods.