An Iterative Algorithm To Compute The Generalized Inverse A(2) T,S Under The Restricted Inner Product

Xingping Sheng
2012 Zenodo  
Let T and S be a subspace of Cn and Cm, respectively. Then for A ∈ Cm×n satisfied AT ⊕ S = Cm, the generalized inverse A(2) T,S is given by A(2) T,S = (PS⊥APT )†. In this paper, a finite formulae is presented to compute generalized inverse A(2) T,S under the concept of restricted inner product, which defined as < A,B >T,S=< PS⊥APT,B > for the A,B ∈ Cm×n. By this iterative method, when taken the initial matrix X0 = PTA∗PS⊥, the generalized inverse A(2) T,S can be obtained within at most mn
more » ... ion steps in absence of roundoff errors. Finally given numerical example is shown that the iterative formulae is quite efficient.
doi:10.5281/zenodo.1072966 fatcat:bjlgd26hdja3dpgqtu263wnlt4