Representations and computations of {2,3∼} and {2,4∼}-inverses in indefinite inner product spaces

We investigate full-rank representations of {2,3∼} and {2,4∼}-inverses with prescribed rank as well as with prescribed range and null space in an indefinite inner product space. In certain particular cases we obtain new results or generalizations related with {2,3} and {2,4}-inverses in a Hilbert (unitary) space. Direct and iterative methods for computing {2,3∼} and {2,4∼}-inverses in an indefinite inner product space are developed. Numerical examples with different metric matrices are presented.