The double splitting iteration method for solving the large indefinite least squares problem

Abstract: Addressing large-scale indefinite least squares (ILS) problem poses notable computational bottlenecks in the field of numerical linear algebra. State-of-the-art iterative schemes for such problems are predominantly constructed upon the single splitting of the coefficient matrix derived from the corresponding normal equation. In this work, we put forward an innovative iterative framework grounded in the double splitting of normal equations tailored for ILS problem. Specifically, we elaborate on a distinct implementations of the double splitting strategy, which offer constructive insights and methodological references for subsequent research on double splitting-based iterative methods. Two numerical experiments further corroborate that the proposed double splitting iterative paradigm outperforms conventional single splitting approaches in both computational efficiency and convergence robustness.