Accelerate overrelaxation methods for rank deficient linear systems

In this paper, we apply accelerated overrelaxation (AOR) methods to find the least square solution of minimal norm to the linear system

Ay=b

where is a matrix of rank r and . We first augment the system to a block 4×4 consistent system, and then split the augmented coefficient matrix by AOR subproper splitting. Intervals for the two relaxation parameters where the AOR iteration matrix is semiconvergent are presented. Also, we provide a method to compute the least square solution of minimal norm to the system.