ON WEIGHTED AVERAGE FAST BLOCK KACZMARZ METHODS FOR SOLVING LARGE CONSISTENT LINEAR SYSTEMS

To solve large consistent linear systems, a weighted average fast block Kaczmarz (WAFBK) method is proposed, which is based on the ideas of greedy distance and weighted average. This method does not require the calculation of pseudoinverse of submatrices. Furthermore, we provide a detailed analysis of the convergence properties of various methods, corresponding to four different weights used in the selection probability criterion. And it has been proven that WAFBK-type methods converge to the unique least-norm solutions of linear systems. Numerical results confirm the effectiveness of the WAFBK-type methods and demonstrate their ability to accelerate the convergence rate of the fast deterministic block Kaczmarz method.