Block-splitting preconditioners for indefinite least squares problem

In this paper, block-splitting preconditioners are proposed for a special class of indefinite least squares problem. The corresponding block-splitting stationary iterative methods are proved to be convergent unconditionally. Furthermore, through the analysis of the spectral properties of the corresponding preconditioned matrix, we obtain all eigenvalues of the preconditioned matrix are real number and located in a positive interval. Numerical experiments show that the proposed block-splitting preconditioned GMRES method outperforms GMRES method without preconditioning.