A generalized successive overrelaxation method for least squares problems

In this paper a new iterative method is given for solving large sparse least squares problems and computing the minimum norm solution to underdetermined consistent linear systems. The new scheme is called the generalized successive overrelaxation (GSOR) method and is shown to be convergent ifA is full column rank. The GSOR method involves a parameter ρ and an auxiliary matrixP. One can choose matrix P so that the GSOR method only involves matrix and vector operations; therefore the GSOR method is suitable for parallel computations. Besides, the GSOR method can be combined with preconditioning techniques, and therefore can be expected to be more effective. This author's work was supported by Natural Science Foundation of Liaoning Province, China.