Symmetric successive overrelaxation methods for solving the rank deficient linear least squares problem

摘要

Symmetric successive overrelaxation (SSOR) methods are developed for finding the least squares solution of minimal norm to the linear systemAx=b,where A∈Cm×n is a matrix of rank r and b∈Cm. By first augmenting the system to a block 4 × 4 consistent system and then splitting the augmented coefficient matrix by subproper SSOR splittings, we obtain intervals for the relaxation parameter in which the subproper SSOR iteration matrix is semiconvergent and a solution for the augmented system. Subsequently, a method for transforming such a solution to the least squares solution of minimal 2-norm is presented.