A CLASS OF COORDINATE DESCENT METHODS WITH ANGLE PROBABILITY FOR SOLVING LINEAR SYSTEMS

In order to resolve large-scale linear systems, we construct the new probability criterion based on the angle between hyperplanes and propose the randomized coordinate descent method with the angle probability criterion. Furthermore, we propose the randomized extended coordinate descent method with the angle probability criterion, which allows to solve underdetermined linear systems. The convergence properties of the two methods are analyzed from the expectation perspective and upper bounds on their convergence rate are derived when the matrix is full rank. Lastly, we conduct numerical experiments to verify the efficacy of our new methods.