On the Construction of a Two-Step Sixth-Order Scheme to Find the Drazin Generalized Inverse

This study introduces a numerically efficient iterative solver for computing the Drazin generalized inverse, addressing a critical need for high-performance methods in matrix computations. The proposed two-step scheme achieves sixth-order convergence, distinguishing it as a higher-order method that outperforms several existing approaches. A rigorous convergence analysis is provided, highlighting the importance of selecting an appropriate initial value to ensure robustness. Extensive numerical experiments validate the analytical findings, showcasing the method’s superior speed and efficiency, making it an advancement in iterative solvers for generalized inverses.