An efficient matrix iteration family for finding the generalized outer inverse

Highlights：

• This article presents a new iterative family having ninth-order convergence for computing the generalized outer inverse.

• The proposed scheme requires only seven matrix multiplications at each iterations, but for the specific parameters, it uses only five matrix multi- plications.

• The detailed theoretical convergence analysis is presented.

• A wide range of random numerical examples is included for comparing the proposed iterations with existing methods.

• It is demonstrated that the proposed methods are computationally effcient and provides an attractive alternative for computing the generalized inverse in practice.