arXiv:2610.07064v1 Announce Type: new Abstract: The development of efficient iterative schemes for approximating the inverse and generalized inverse matrices is important in my research fields. To this end, a family of fourth-order matrix iterative schemes for approximating the inverse and generalized inverse matrices is established by incorporating an appropriate weight function into the scalar Heun method. Moreover, a fifth-order matrix iterative scheme is obtained as a particular member of the proposed family. Under suitable conditions, the theoretical order of convergence is determined for the proposed family, whose stable members are identified through dynamical analysis. To assess their performance and verify the consistency of the theoretical results, some numerical tests are performed on matrices of different sizes.