On convergence of residual-based extended randomized Kaczmarz methods for matrix equations
This work addresses matrix equation solving for computational mathematics, but it is incremental as it builds on existing Kaczmarz methods.
The paper tackles solving inconsistent matrix equations by proposing a dual-space residual-based randomized extended Kaczmarz method and its version with Nesterov momentum, showing that the new methods are much more effective than existing ones, especially with momentum, as demonstrated in numerical experiments.
In this paper, for solving inconsistent matrix equations we propose a dual-space residual-based randomized extended Kaczmarz method and its version with Nesterov momentum. Without the full column rank assumptions on coefficient matrices, we provide a thorough convergence analysis, and derive upper bounds for the convergence rates of the new methods. A feasible range for the momentum parameters is determined. Numerical experiments demonstrate that the proposed methods are much more effective than the existing ones, especially the method with momentum.