On Cyclic Block Coordinate Descent Method for Solving Large Inconsistent Linear Systems

For solving large inconsistent linear systems, we research a novel format to enhance the numerical stability and control the complexity of the model. Based on the idea of two subspace iterations, we propose the max-residual two subspace coordinate descent (M2CD) method. To accelerate the convergence rate, we further present the cyclic block coordinate descent (CBCD) method. The convergence properties of these methods are analyzed, and their effectiveness is illustrated by numerical examples.