Semi-extensive shift-splitting preconditioner for indefinite least squares problem

We present a semi-extensive shift-splitting preconditioner for a class of large and sparse indefinite least squares problem. The preconditioner is derived from an unconditionally convergent iterative method. Additionally, theoretical analysis proves that all eigenvalues of the preconditioned matrix are located in the positive interval $(0, 2)$. Numerical experiments demonstrate that the semi-extensive shift-splitting preconditioner significantly outperforms existing preconditioners in terms of both algorithm running time and number of iterations. 2000 MSC: 65F10, 65F15